Motion — Cambridge IGCSE Physics 0625 Revision Notes & Topical Questions

Section 1 of 51Speed

Speed

Speed distance travelled per unit time, a scalar

Equation

• Equation v = s ÷ t for constant speed

Units

• Units v in metres per second (m/s), s in metres (m) and t in seconds (s)

Formula triangle

• Formula triangle cover the quantity to find

Section 2 of 51Average speed

1Average speed

Average speed total distance travelled ÷ total time taken

2Variable journeys

• Variable journeys a car speeds up, slows down and stops, so average speed is more useful than instantaneous speed

3Typical values

• Typical values walking 1.5 m/s, running 3 m/s, cycling 6 m/s, a plane about 250 m/s

Section 3 of 51Velocity

Velocity

Velocity speed in a stated direction, a vector

Equation

• Equation v = s ÷ t, where s is displacement

Direction

• Direction it must be stated with the answer

Sign

• Sign either direction can be positive if the opposite direction is negative and the choice is consistent

Section 4 of 51Acceleration

Acceleration

Acceleration the change in velocity per unit time, the rate of change of velocity

Equation

• Equation a = Δv ÷ Δt
  What the symbols mean: a = acceleration (m s⁻²) · v = final velocity · u = initial velocity (m s⁻¹) · Δv = change in velocity · t = time taken (s)

Units

• Units metres per second squared (m/s²)

Change in velocity

• Δv = v − u, where v is the final and u the initial velocity

Section 5 of 51Distance-time graphs

Gradient

• Gradient the gradient of a distance-time graph is the speed

Horizontal line

• Horizontal line the object is stationary

Straight sloping line

• Straight sloping line constant speed

Curve

• Curve changing speed, with a steeper curve meaning increasing speed

Section 6 of 51Speed-time graphs

Gradient

• Gradient the gradient of a speed-time graph is the acceleration

Horizontal line

• Horizontal line constant speed

Straight sloping line

• Straight sloping line constant acceleration

Area under the graph

• Area under the graph it equals the distance travelled

Section 7 of 51Free fall

1Acceleration of free fall

• Acceleration of free fall g is about 9.8 m/s² when air resistance is absent

2Terminal velocity

• Terminal velocity an object falling through air reaches constant speed when air resistance equals weight

Section 8 of 51More from the specification

More from the specification

Speed and velocity

• Speed and velocity speed is distance over time with no direction, whereas velocity is a vector giving displacement per unit time.

Gradient of a distance-time graph

• Gradient of a distance-time graph the slope represents speed, and a steeper line means faster motion;
  • a flat line means the object is stationary.

Falling object and skydiver

• Falling object and skydiver weight accelerates a falling object until air resistance rises to equal it,
  • giving terminal velocity with zero resultant force.

Decreasing gradient

• Decreasing gradient a curve that flattens on a speed-time graph shows the acceleration is decreasing as the resistive force grows.

Speed and velocity

• Speed and velocity speed is distance over time with no direction, whereas velocity is a vector giving displacement per unit time.

Gradient of a distance-time graph

• Gradient of a distance-time graph the slope represents speed, and a steeper line means faster motion;
  • a flat line means the object is stationary.

Falling object and skydiver

• Falling object and skydiver weight accelerates a falling object until air resistance rises to equal it,
  • giving terminal velocity with zero resultant force.

Decreasing gradient

• Decreasing gradient a curve that flattens on a speed-time graph shows the acceleration is decreasing as the resistive force grows.

Resultant force

• Another name for net force.

Gravitational field

• Region where mass experiences gravitational force.

Field strength

• G = F_g/m.

Section 9 of 51Speed

Definition

• Definition speed is the distance travelled per unit time.
• Speed is a scalar because it has magnitude only.

Equation

• Equation for constant speed, v = s ÷ t.
  What the symbols mean: v = speed (m s⁻¹) · d or s = distance (m) · t = time (s)
• v is speed in metres per second (m/s).
• s is distance in metres (m).
• t is time in seconds (s).

Formula triangle

• Formula triangle cover the quantity you want and the arrangement of the other two is revealed.
• Distance = speed × time and time = distance ÷ speed.

Section 10 of 51Average speed

Why it is used

• Why it is used the speed of an object often varies during a journey.
• A car speeds up, slows down and stops at junctions and traffic lights.

Equation

• Equation average speed = total distance travelled ÷ total time taken.
• Both the whole distance and the whole time, including stops, are used.

Typical values

• Typical values these help check whether an answer is sensible.
• Walking is about 1.5 m/s, running about 3 m/s and cycling about 6 m/s.
• An experienced hiker averages about 2.0 m/s and a bumble bee can reach 4.5 m/s.

Section 11 of 51Velocity

1Definition

• Definition velocity is speed in a given direction.
• Velocity is a vector because it has magnitude and direction.

2Equation

• Equation v = s ÷ t, where s is displacement.
• Displacement is a vector, so velocity must be given with a direction.

3Stating direction

• Stating direction direction can be given in words or by a sign.
• 20 m/s east and −20 m/s are both valid ways to give a velocity.
• Positive is normally the direction of the initial motion, to the right or upwards.

4Same speed, different velocity

• Same speed, different velocity two cars driving in opposite directions at 20 m/s have equal speeds but different velocities.

Section 12 of 51Acceleration

Definition

• Definition acceleration is the change in velocity per unit time.
• It is the rate of change of velocity and is measured in m/s².

Equation

• Equation a = Δv ÷ t.
  What the symbols mean: a = acceleration (m s⁻²) · v = final velocity · u = initial velocity (m s⁻¹) · Δv = change in velocity · t = time taken (s)
• Δv is the change in velocity in m/s and t is the time taken in seconds.

Change in velocity

• Δv = v − u.
• v is the final velocity and u is the initial velocity.

Section 13 of 51Speeding up, slowing down and changing direction

Motion	Change in velocity	Acceleration
Speeding up	Velocity increases in the direction of motion	Positive
Slowing down	Velocity decreases	Negative (deceleration)
Changing direction	Velocity changes because direction changes	Non-zero, even at constant speed

Meaning of the unit

• Meaning of the unit m/s² means the velocity changes by that many metres per second every second.

Decreasing but positive

• Decreasing but positive an object whose acceleration is falling but still positive is still speeding up, only more slowly.

Section 14 of 51Choosing a positive direction

Free choice

• Free choice any direction may be positive provided the opposite direction is negative.
• Once a positive direction is chosen it must be used throughout.

Effect on acceleration

• Effect on acceleration a negative acceleration can mean slowing down or speeding up in the negative direction.
• A car moving right and slowing has negative acceleration relative to the right.
• A car moving left and speeding up also has negative acceleration relative to the right.

Section 15 of 51More from the specification

More from the specification

Distance-time graph interpretation

• On a distance-time graph, the gradient represents speed; a straight line indicates constant speed,
• while a curved line represents changing speed.
  • (acceleration or deceleration)

Speed-time graph analysis

• On a speed-time graph, the gradient represents acceleration,
• and the area under the line or curve represents the total distance travelled by the moving object.

Air resistance and terminal velocity

• When an object falls, downward weight is initially greater than upward air resistance force,
• causing acceleration;
• as speed increases, resistive drag rises until forces balance and speed becomes constant.

Non-linear motion graphs and changing gradients

• A curve on a speed-time graph illustrates non-uniform acceleration, occurring when resultant force decreases as air resistance increases with velocity.

Distance-time graph interpretation

• On a distance-time graph, the gradient represents speed; a straight line indicates constant speed,
• while a curved line represents changing speed.
  • (acceleration or deceleration)

Speed-time graph analysis

• On a speed-time graph, the gradient represents acceleration,
• and the area under the line or curve represents the total distance travelled by the moving object.

Air resistance and terminal velocity

• When an object falls, downward weight is initially greater than upward air resistance force,
• causing acceleration;
• as speed increases, resistive drag rises until forces balance and speed becomes constant.

Non-linear motion graphs and changing gradients

• A curve on a speed-time graph illustrates non-uniform acceleration, occurring when resultant force decreases as air resistance increases with velocity.

Speed-time graph

• Graph of speed against time.

Distance-time graph

• Graph of distance against time showing movement.

Resultant force

• Another name for net force.

Gravitational field

• Region where mass experiences gravitational force.

Field strength

• G = F_g/m.

Gradient

• Slope of a graph line.

Resistance

• Opposition to current, R = V / I, in ohms (Ω).

Weight

• Gravitational force on a mass.

Terminal

• Connection point of a cell, labelled + or −.

Section 16 of 51What a distance-time graph shows

Purpose

• Purpose it describes the motion of an object and allows its speed to be calculated.
• Time is on the x-axis and distance is on the y-axis.

Gradient is speed

• Gradient is speed the gradient at any point equals the speed of the object.
• A steeper slope means a greater speed.
• A shallower slope means a slower speed.

Section 17 of 51Reading the shape of the line

Shape of line	Gradient	Motion
Horizontal straight line	Zero	Stationary, distance does not change
Straight sloping line	Constant	Constant speed
Curve getting steeper	Increasing	Speeding up (accelerating)
Curve getting shallower	Decreasing	Slowing down (decelerating)

• Two straight lines
  • two objects with straight lines move at constant speeds, but the steeper one is faster.

Section 18 of 51Plotting a distance-time graph

1

Label the x-axis with time and the y-axis with distance, including units.

2

Choose sensible scales so the graph fills more than half of the grid.

3

Plot the points from the data.

4

Join the points with straight lines for constant speed or with curves where the speed changes.

Section 19 of 51Calculating speed from the gradient

1

Choose a straight section of the line.

2

Draw the largest gradient triangle possible within that section.

3

Read the change in distance (Δy) and the change in time (Δx) from the axes.

4

Convert both to standard units, metres and seconds.

5

Calculate speed = gradient = Δy ÷ Δx.

• Multi-section graphs
  • never use the whole line if the graph has more than one section.

Section 20 of 51Describing a journey

1Moving away

• Moving away the distance increases while the line slopes upwards.

2Stopped

• Stopped a flat section shows the object is stationary.

3Returning

• Returning a line sloping down shows the distance from the start decreasing.

4Comparing sections

• Comparing sections the steeper the section, the faster the movement.
• A student running home covers the same distance as the walk out in less time, so the return section is steeper.

Section 21 of 51Reading axes and units

1Check the axes first

• Check the axes first distances and times are not always in metres and seconds.
• A graph may use kilometres on the y-axis and minutes on the x-axis.
• Convert before calculating a speed in m/s.

2Scale per square

• Scale per square work out what each small square represents before reading values.
• Count squares between labelled values and divide.

Section 22 of 51Total distance versus distance from start

Distance from start

• Distance from start the y-axis value is how far the object is from the origin, not how far it has travelled in total.
• A line returning to zero means the object is back at the start.

Total distance travelled

• Total distance travelled add the length of each leg of the journey.
• 0.3 km out and 0.3 km back is a total distance of 0.6 km even though the final position is zero.

Average speed of a trip

• Average speed of a trip divide the total distance travelled by the total time including any rest.

Section 23 of 51Comparing two objects on one graph

Observation	Meaning
Lines cross	The objects are at the same distance at the same time
One line steeper	That object moves faster
Parallel lines	The objects move at the same speed
One line starts higher at t = 0	That object started further from the origin

Section 24 of 51More from the specification

More from the specification

Terminal velocity of falling skydiver

• Terminal velocity of falling skydiver a falling skydiver accelerates until upward air resistance force balances downward weight, achieving zero resultant acceleration.

Speed-time graph slope and acceleration

• Speed-time graph slope and acceleration gradient slopes on speed-time graphs represent acceleration,
  • where negative gradient slopes denote deceleration or braking.

Vector velocity and motion direction

• Vector velocity and motion direction velocity measures rate of displacement change in a specified direction,
  • allowing positive and negative directional conventions.

Speed-Time and Velocity-Time Graphs

• On a speed-time graph, the gradient represents the magnitude of acceleration,
• while the area under the line represents the total distance travelled; velocity includes direction,
• so motion in the opposite direction is measured as negative velocity.

Terminal Velocity of a Falling Skydiver

• When a skydiver jumps from an aircraft, their downward weight force initially exceeds upward air resistance,
• causing downward acceleration;
• as speed increases, air resistance increases until it balances weight,
• resulting in zero net force and constant terminal velocity.

Forces and Changes in Motion

• An object's velocity remains constant unless acted upon by a resultant unbalanced force; the time taken to change velocity depends inversely on the magnitude of the applied resultant force (F = m·a).
  What the symbols mean: F = resultant force (N) · m = mass (kg) · a = acceleration (m s⁻²)

Resultant force

• Another name for net force.

Gravitational field

• Region where mass experiences gravitational force.

Field strength

• G = F_g/m.

Velocity

• Rate of change of displacement.

Resistance

• Opposition to current, R = V / I, in ohms (Ω).

Weight

• Gravitational force on a mass.

Terminal

• Connection point of a cell, labelled + or −.

Speed-time graph

• Graph of speed against time.

Terminal velocity

• Constant speed when air resistance equals weight.

Section 25 of 51Reading a speed-time graph

Purpose

• Purpose it describes the speed of an object and allows acceleration to be found.
• Time is on the x-axis and speed is on the y-axis.

Gradient is acceleration

• Gradient is acceleration a steeper line means a greater acceleration.
• A shallower line means a smaller acceleration.

Sign of the gradient

• Sign of the gradient the slope direction shows speeding up or slowing down.
• An upward slope is positive acceleration and speed is increasing.
• A downward slope is negative acceleration, or deceleration.

Section 26 of 51Shapes of the line

Shape	Acceleration	Motion
Horizontal line above zero	Zero	Constant speed
Horizontal line at zero	Zero	Stationary
Straight line sloping up	Constant and positive	Steadily speeding up
Straight line sloping down	Constant and negative	Steadily slowing down

Section 27 of 51Plotting a speed-time graph

1

Label the x-axis with time and the y-axis with speed.

2

Choose sensible scales so the graph fills more than half of the grid.

3

Plot the points from the data.

4

Join them with horizontal lines for constant speed and sloping straight lines where speed changes.

Section 28 of 51Distance from the area under the graph

Key idea

• Key idea the area under a speed-time graph equals the distance travelled.
• The total area gives the total distance.
• The area over a chosen time interval gives the distance in that interval.

Area formulae

• Area formulae split the region into triangles and rectangles.
• TriangleA = ½ × base × height.
• RectangleA = base × height.

Section 29 of 51Method for a multi-section graph

1

State that distance equals area under the graph.

2

Label each enclosed shape as a triangle or rectangle.

3

Calculate each area using the correct formula.

4

Add the areas to find the total distance.

5

For a time interval, add only the areas lying above that interval.

• Trapezium regions
  • split into a rectangle plus a triangle.

Section 30 of 51Connecting gradient, area and units

Graph	Gradient gives	Area gives
Distance-time	Speed	Nothing useful at this level
Speed-time	Acceleration	Distance travelled

1Units check

• Units check speed in m/s multiplied by time in s gives distance in m.
• This confirms why the area under the graph is a distance.

2Converting first

• Converting first if time is in minutes or speed in km/h, convert before finding any area.

Section 31 of 51Describing a whole journey from the graph

1Sloping up

• Sloping up the object accelerates, with the size of the acceleration given by the gradient.

2Flat section

• Flat section the object travels at a constant speed.

3Sloping down

• Sloping down the object decelerates.

4Touching zero

• Touching zero the object has stopped at that moment.

Section 32 of 51Distance, average speed and maximum speed

1Distance in a stated interval

• Distance in a stated interval find the area under the graph over that interval only.

2Total distance

• Total distance find the area under the whole line.

3Average speed

• Average speed total distance from the area divided by the total time.

4Maximum speed

• Maximum speed the highest point on the graph.

Section 33 of 51More from the specification

More from the specification

Terminal Velocity Dynamics

• A falling object accelerates downwards under weight until air resistance equals weight,
• resulting in zero resultant force and constant terminal velocity.

Velocity-Time Graph Gradient

• On a velocity-time graph for a falling body, a curve with decreasing gradient represents decreasing acceleration as drag force increases.

Distance Travelled Calculation

• The total distance covered by a moving object is determined by measuring the area under the velocity-time graph over the time taken.

Vector Velocity vs Scalar Speed

• Speed is a scalar quantity measured without direction, whereas velocity is a vector that specifies both magnitude and direction of motion.

Resultant force

• Another name for net force.

Gravitational field

• Region where mass experiences gravitational force.

Field strength

• G = F_g/m.

Velocity

• Rate of change of displacement.

Resistance

• Opposition to current, R = V / I, in ohms (Ω).

Weight

• Gravitational force on a mass.

Terminal

• Connection point of a cell, labelled + or −.

Section 34 of 51Shape of the graph tells the acceleration

Constant acceleration

• Constant acceleration the graph is a straight line.
• The speed changes by the same amount in equal intervals of time, such as 5 m/s every 20 s.

Gradient sign

• Gradient sign the gradient is positive for speeding up and negative for slowing down.

Changing acceleration

• Changing acceleration the graph is a curve.

Section 35 of 51Types of curved graph

Curve	Speed	Acceleration	Evidence
Getting steeper upwards	Increasing at an increasing rate	Increasing and positive	Time for each 5 m/s gain gets shorter
Getting shallower upwards	Increasing at a decreasing rate	Decreasing but positive	Time for each 5 m/s gain gets longer
Downward, getting shallower	Decreasing at a decreasing rate	Deceleration getting smaller	Time for each 5 m/s loss gets longer

Section 36 of 51Acceleration from a straight line

1

Choose a straight section of the graph.

2

Draw a large gradient triangle on it.

3

Read the change in speed Δv and the change in time Δt.

4

Use a = Δv ÷ Δt, giving the answer in m/s².

Section 37 of 51Acceleration from a curve

Tangent

• Tangent a straight line that matches the slope of the curve at one point.
• Draw it so it touches the curve only at the chosen time.

Gradient of the tangent

• Gradient of the tangent it gives the instantaneous acceleration at that moment.
• Use a = Δy ÷ Δx on the tangent with a large triangle.

Section 38 of 51Method for finding acceleration

1

State that acceleration is the gradient of a speed-time graph.

2

Identify whether the section is straight or curved.

3

For a straight line draw a large triangle and read Δv and Δt.

4

For a curve draw a tangent at the required time and use its gradient.

5

Substitute into a = Δv ÷ Δt and include units of m/s².

6

Interpret the sign of the answer in words.

Section 39 of 51Describing acceleration in words

Constant acceleration

• Constant acceleration the line is straight and the speed rises by equal amounts each second.

Increasing acceleration

• Increasing acceleration the curve steepens as time passes.
• The speed gains each 5 m/s in shorter and shorter times.

Decreasing acceleration

• Decreasing acceleration the curve flattens as time passes.
• The speed still increases, but each 5 m/s gain takes longer, as for a skydiver approaching terminal velocity.

Zero acceleration

• Zero acceleration the line is flat and speed is constant.

Section 40 of 51Link to forces

Resultant force

• Resultant force acceleration found from the graph can be used in F = ma.
• A 70 kg cyclist accelerating at 1 m/s² needs a resultant force of 70 N.

Skydiver

• Skydiver the gradient of the speed-time curve falls to zero at terminal velocity.

Braking

• Braking a negative gradient with a larger magnitude means harder braking.

Section 41 of 51More from the specification

More from the specification

Distance-Time Graphs and Speed

• On a distance-time graph, the gradient represents the instantaneous speed of the moving object;
  • a steeper slope represents greater speed,
• while a horizontal line indicates a stationary object.

Average Speed Formula

• The average speed of an object is defined as total distance travelled divided by total time taken (v = d / t), expressed in metres per second (m s⁻¹).

Velocity as a Vector Quantity

• Velocity is speed in a specified direction;
  • changing either the speed or direction of motion results in a change in velocity, indicating acceleration.

Terminal Velocity and Air Resistance

• When a falling object's downward weight is balanced by upward air resistance, resultant force becomes zero and the object falls at constant terminal velocity.

Distance-time graph

• Graph of distance against time showing movement.

Average speed

• Total distance divided by total time.

Gravitational field

• Region where mass experiences gravitational force.

Field strength

• G = F_g/m.

Distance

• Total length of path travelled, a scalar.

Resistance

• Opposition to current, R = V / I, in ohms (Ω).

Weight

• Gravitational force on a mass.

Section 42 of 51Acceleration of free fall

Definition

• Definition free fall is motion where only weight acts, and without air resistance all objects fall with the same acceleration.
• Near Earth's surface this acceleration, g, is about 9.8 m/s².
• Velocity increases by about 9.8 m/s every second of fall.

Weight

• W = mg.
  What the symbols mean: W = weight (N) · m = mass (kg) · g = gravitational field strength (9.81 N kg⁻¹ on Earth)
• W is weight in newtons, m is mass in kilograms and g is gravitational field strength in N/kg.

Section 43 of 51Why mass does not matter in a vacuum

1

In a vacuum there are no particles, so there is no air resistance.

2

The only force on the falling object is its weight, W = mg.

3

Newton's second law gives a = F ÷ m = mg ÷ m.

4

The masses cancel, so a = g for every object.

1Evidence

• Evidence a hammer and a feather dropped together on the Moon landed at the same time.

2Negligible air resistance

• Negligible air resistance if resistance is small enough to ignore, the object behaves as if it falls in a vacuum.

Section 44 of 51Falling through air or liquid

Two forces

• Two forces weight acts downwards and air resistance acts upwards.
• Air resistance comes from collisions with air particles.
• It increases as speed increases.

Liquids

• Liquids a liquid exerts a drag force that opposes motion and also increases with speed.

Terminal velocity

• Terminal velocity when air resistance equals weight the forces are balanced.
• The resultant force is zero, so acceleration stops and speed is constant.

Section 45 of 51A skydiver's fall in stages

1

At the start only weight acts, so the skydiver accelerates downwards.

2

As speed rises, air resistance rises, so the resultant force falls and acceleration decreases.

3

Air resistance reaches the weight, so the resultant force is zero and terminal velocity is reached.

4

The parachute opens, greatly increasing the surface area and air resistance.

5

Air resistance now exceeds weight, so the resultant force is upwards and the skydiver decelerates while still falling.

6

As speed falls, air resistance falls until it again equals weight and a lower terminal velocity is reached.

Section 46 of 51Reading the skydiver's graph

Reading the skydiver's graph

Horizontal sections

• Horizontal sections these show periods of terminal velocity.

Steep early section

• Steep early section the speed climbs quickly while weight is the main force.

Drop after the parachute opens

• Drop after the parachute opens the speed falls to a smaller constant value.

Section 47 of 51Weight, mass and gravitational field strength

Weight, mass and gravitational field strength

Weight

• Weight the gravitational force on a mass, measured in newtons.
• W = mg, so a 60 kg skydiver weighs 588 N on Earth.

Gravitational field strength

• Gravitational field strength g = W ÷ m is the force per unit mass.
• Near Earth g is 9.8 N/kg, which equals the acceleration of free fall in m/s².

Mass stays constant

• Mass stays constant only the weight changes with location.
• On the Moon g is about 1.6 N/kg, so weight is about six times smaller.

Section 48 of 51Forces and acceleration during a fall

Stage	Weight	Air resistance	Resultant force	Motion
Start of fall	mg downwards	Very small	Large, downwards	Large acceleration
Speed increasing	mg downwards	Growing	Smaller, downwards	Acceleration decreasing
Terminal velocity	mg downwards	Equal to weight	Zero	Constant speed
Parachute opens	mg downwards	Greater than weight	Upwards	Decelerating

Section 49 of 51More from the specification

1Gradient of a Distance-Time Graph

• On a distance-time graph, the gradient represents the speed of the moving object;
  • a constant positive gradient indicates steady motion at constant speed.

2Speed-Time Graph and Distance Travelled

• On a speed-time graph, the total area enclosed under the curve represents the total physical distance travelled by the object during that time interval.

3Interpreting Acceleration on Graphs

• The gradient of a speed-time graph represents acceleration; a positive gradient indicates increasing speed,
• while a horizontal line represents constant speed.

4Average Speed vs Velocity

• Average speed is calculated by dividing total distance travelled by total elapsed time,
• whereas velocity is a vector that incorporates direction of travel.

5Speed-time graph

• Graph of speed against time.

6Distance-time graph

• Graph of distance against time showing movement.

7Average speed

• Total distance divided by total time.

8Gradient triangle

• A right-angled triangle drawn on a line to find Δy and Δx.

9Gradient

• Slope of a graph line.

10Distance

• Total length of path travelled, a scalar.

Section 50 of 51Key terms

Term	Meaning
Speed	Distance per unit time.
Velocity	Speed in a given direction.
Acceleration	Change in velocity per unit time.
Gradient	Steepness of a graph line.
Terminal velocity	Constant speed when air resistance equals weight.
Free fall	Falling under weight alone.

Term	Meaning
Speed	Distance travelled per unit time, a scalar.
Average speed	Total distance travelled divided by total time taken.
Velocity	Speed in a given direction, a vector.
Acceleration	Change in velocity per unit time.
Deceleration	Negative acceleration, when an object slows down.
Instantaneous speed	The speed at a particular moment.

Term	Meaning
Distance-time graph	A graph of distance against time whose gradient gives speed.
Gradient	The change in y divided by the change in x for a line.
Stationary	Not moving, so the speed is zero.
Gradient triangle	A right-angled triangle drawn on a line to find Δy and Δx.
Constant speed	Equal distances covered in equal times, shown by a straight line.

Term	Meaning
Speed-time graph	A graph of speed against time whose gradient gives acceleration and whose area gives distance.
Area under the graph	The distance travelled when the graph is speed against time.
Uniform acceleration	Constant acceleration, shown by a straight sloping line.
Deceleration	Negative acceleration, shown by a downward slope.
Base	The horizontal side of a shape, here an interval of time.

Term	Meaning
Gradient	Change in y divided by change in x, giving acceleration on a speed-time graph.
Tangent	A straight line touching a curve at one point and matching its slope there.
Instantaneous acceleration	The acceleration at one moment, found from a tangent.
Constant acceleration	Equal speed changes in equal times, shown by a straight line.
Uniform	Not changing with time.

Term	Meaning
Free fall	Motion under the influence of weight alone.
Acceleration of free fall	About 9.8 m/s2 near Earth's surface.
Air resistance	A frictional force from collisions with air particles that opposes motion.
Terminal velocity	The constant speed reached when air resistance equals weight.
Drag	A resistive force from a fluid that opposes motion.
Vacuum	A space containing no matter.

Section 51 of 51Exam technique

1

Mixing up the two graphs — the gradient is speed on a distance-time graph and acceleration on a speed-time graph.

2

Using the formula for speed with an average of two speeds — use total distance divided by total time.

3

Writing deceleration as a positive speed change — it is a negative acceleration.

4

Using the area on a distance-time graph — area under a speed-time graph gives distance.

1

Using hours or minutes in a speed calculation — convert to seconds when the speed is in m/s.

2

Calling velocity and speed the same — velocity needs a direction, so it can be negative.

3

Taking average speed as the mean of the highest and lowest speeds — it is total distance divided by total time.

4

Thinking a car turning a corner at constant speed is not accelerating — a change of direction is a change of velocity.

1

Reading the height of the line as speed — speed is the gradient, not the distance value.

2

Saying a horizontal line means constant speed — on a distance-time graph it means the object is stationary.

3

Using a tiny gradient triangle — a large triangle gives a more accurate answer.

4

Forgetting to change km and minutes to m and s when the answer must be in m/s.

1

Using the gradient to find distance — the gradient gives acceleration, the area gives distance.

2

Reading a flat line on a speed-time graph as stopped — it means constant speed unless the line is at zero.

3

Using the full graph when a time interval is asked for — only the area over that interval counts.

4

Forgetting the half in the triangle formula — a triangle is ½ × base × height.

1

Measuring the gradient of a curve between two points on the curve — draw a tangent at the point instead.

2

Thinking a flat section means the object is accelerating — zero gradient means zero acceleration.

3

Saying a curve flattening means slowing down — if the speed is still above the previous value it is still speeding up, but with less acceleration.

4

Giving acceleration in m/s — the unit is m/s².

1

Confusing air resistance with air pressure — resistance is a frictional force opposing motion.

2

Saying a skydiver moves upwards when the parachute opens — they decelerate but still fall.

3

Thinking heavier objects always fall faster — in a vacuum all objects fall with acceleration g.

4

Saying terminal velocity means no forces act — the forces are balanced, not absent.