1.2Physical quantities and kinematics

Kinematics

5 min read 10 parts Lesson 4 of 22 1 quiz

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Lesson summary

1.2 Kinematics — AS PHYSICS 9702 notes: Define displacement, velocity and acceleration, interpret motion graphs and apply the equations of motion to straight-line and projectile motion.Distance = how far an object travels, a scalar.Displacement = change in position from the start…

Average speed = total distance ÷ time taken
What the symbols mean
Average velocity is not average speed in a given direction
Distance-time
Displacement-time
The y-intercept is the initial position

Section 1 of 10Distance, displacement, speed and velocity

1Distance

Distance how far an object travels, a scalar.

2Displacement

Displacement change in position from the start with direction, a vector.

3Average speed

Average speed total distance ÷ time taken

unit m s^-1.

4Velocity

Velocity rate of change of displacement: v_avg = Δx ÷ Δt, and for uniform acceleration v_avg = (u + v) ÷ 2.

5Acceleration

Acceleration rate of change of velocity: a = Δv ÷ Δt, with Δv = v − u and unit m s^-2.

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)

6Average velocity is not average speed in a given direction

Average velocity is not average speed in a given direction speed uses distance and velocity uses displacement.

Section 2 of 10Distance-time and displacement-time graphs

Distance-time and displacement-time graphs

Distance-time

Distance-time gradient is speed, a straight line is constant speed, a curve is acceleration, a horizontal line is rest,
- and the gradient is never negative.

Displacement-time

Displacement-time gradient is velocity;
- positive means motion in the positive direction and negative the opposite direction.

The y-intercept is the initial position

The y-intercept is the initial position and the area under either graph is meaningless.

Section 3 of 10Velocity-time and speed-time graphs

Velocity-time and speed-time graphs

Gradient is acceleration

Gradient is acceleration the y-intercept is the initial value.

Straight line

Straight line uniform acceleration, a curve is non-uniform acceleration and a horizontal line is constant velocity.

Area under a v-t graph is displacement

Area under a v-t graph is displacement and under a speed-time graph is distance.

Area below the axis counts as negative displacement

Area below the axis counts as negative displacement take magnitudes to find total distance.

Area under an acceleration-time graph

Area under an acceleration-time graph the change in velocity.

Section 4 of 10Tangents and curved graphs

Tangents and curved graphs

The instantaneous value

The instantaneous value is the gradient of the tangent to the curve at that point.

Draw the tangent with a ruler touching the curve at one point

Draw the tangent with a ruler touching the curve at one point and take a large triangle on the tangent.

Area of a curved graph

Area of a curved graph estimate by counting squares or by thin strips.

Section 5 of 10Deriving the equations of motion

1For constant acceleration there are four equations

For constant acceleration there are four equations v = u + at; s = ½(u + v)t; s = ut + ½at²; v² = u² + 2as.
What the symbols mean: v = final velocity (m s⁻¹) · u = initial velocity (m s⁻¹) · a = acceleration (m s⁻²) · t = time (s)

v u + at

from the definition of acceleration.

½(u + v)t

from the area of the trapezium under the v-t graph.
What the symbols mean: s = displacement (m) · u = initial velocity · v = final velocity (m s⁻¹) · t = time (s); (u + v)/2 is the average velocity

s ut + ½at2

from a rectangle ut plus a triangle ½at².
What the symbols mean: s = displacement (m) · u = initial velocity (m s⁻¹) · a = acceleration (m s⁻²) · t = time (s)

5v2

v2 u2 + 2as

by eliminating t.
What the symbols mean: v = final velocity · u = initial velocity (m s⁻¹) · a = acceleration (m s⁻²) · s = displacement (m)

6They apply only when acceleration is constant

They apply only when acceleration is constant in a straight line.

Section 6 of 10Solving kinematics problems

Write the known and unknown variables s, u, v, a and t, using context for hidden values.

For vertical motion a = ±9.81 m s^-2; starting or finishing at rest gives u = 0 or v = 0.

Choose the equation that contains the unknown and the three known quantities.

Convert to SI units, substitute and rearrange.

Check the unit and whether the answer is sensible.

Section 7 of 10Projectile motion

Projectile motion

Vertical and horizontal motions are independent

Vertical and horizontal motions are independent evaluated separately.

After release the only force is gravity

After release the only force is gravity horizontal acceleration is zero and vertical acceleration is g = 9.81 m s^-2 downward.

Time of flight, maximum height and range

Time of flight, maximum height and range are the quantities to find;
- the vertical velocity is zero at maximum height.

Three cases

Three cases vertical projection, horizontal projection and projection at an angle.

At an angle

At an angle resolve u into u cos θ and u sin θ.

Section 8 of 10Acceleration of free fall experiment

Acceleration of free fall experiment

Drop a steel ball-bearing from an electromagnet through two light gates a height h apart.

The independent variable is h

The independent variable is h the dependent variable is the time t;
- controls are the same ball and electromagnet.

From s

From s ut + ½at2

2h ÷ t = gt + 2u, so plot 2h ÷ t against t: the gradient is g.

Systematic error

Systematic error residual magnetism may lengthen t.

Random errors

Random errors the 1 mm metre rule, parallax and the ball not falling through the gate centre, reduced by repeats.

Safety

Safety no water near the electromagnet, a cushion for the ball and a G-clamp on the stand.

Section 9 of 10Key terms

Term	Meaning
Displacement	Change in position in a given direction, a vector.
Velocity	Rate of change of displacement.
Acceleration	Rate of change of velocity.
Kinematic equations	Four equations for motion in a straight line with constant acceleration.
Projectile	An object moving under gravity alone.
Time of flight	How long a projectile is in the air.
Range	The horizontal distance travelled by a projectile.
Tangent	A straight line touching a curve at one point, giving the instantaneous gradient.

Section 10 of 10Exam technique

Using distance instead of displacement when calculating velocity.

Applying the equations of motion when acceleration is not constant.

Forgetting that deceleration is negative as an object rises.

Reading the gradient of a velocity-time graph as velocity — it is acceleration.

Physics 0625 & 9702 SUVAT Mastery Graph Interpretation

Constant Acceleration Equations (SUVAT) & Slopes

v = u + at | s = ut + ½at² | v² = u² + 2as | s = ½(u + v)t

Displacement-Time Graph: Gradient = Velocity (curve = accelerating).
Velocity-Time Graph: Gradient = Acceleration; Area under curve = Distance travelled / Displacement.
Free Fall in vacuum: a = g ≈ 9.81 m/s² downwards (air resistance negligible).