2.1.1Forces and Motion
Displacement, Velocity and Acceleration
5 min read 10 parts Lesson 4 of 66 1 quiz
Lesson summary
2.1.1 Displacement, Velocity and Acceleration — AS PHYSICS 9702 notes: Define distance, displacement, speed, velocity and acceleration and use their equations and sign conventions.Distance = a measure of how far an object travels; it is the total length of the path and is a scala…
- Displacement is positive or negative
- SI unit m s-1
- A car's speedometer
- Average velocity vavg = Δs ÷ Δt
- For uniform acceleration
- Instantaneous velocity
Section 1 of 10Distance and displacement
1Distance
Distance a measure of how far an object travels; it is the total length of the path and is a scalar.
2Displacement
Displacement the change in position of an object, that is its distance from the starting position in a stated direction; it is a vector.
3Displacement is positive or negative
- Displacement is positive or negative once a positive direction has been chosen, for example up or to the right.
4
A 300 m race on a 400 m track gives a distance of 300 m but a displacement of 100 m.
- A full 400 m lap gives a displacement of zero.
Section 2 of 10Speed
Speed
Speed the distance an object travels per unit time; it is a scalar with magnitude only.
Average speed = total distance ÷ time taken.
SI unit m s−1
- SI unit m s−1 other units such as km h-1 or mph can be used when more appropriate.
A car's speedometer
- A car's speedometer shows instantaneous speed.
Section 3 of 10Velocity
Velocity
Velocity
Velocity the rate of change of displacement; it is a vector and is speed in a given direction.
Average velocity vavg
Δs ÷ Δt
- total displacement divided by total time.
For uniform acceleration
- For uniform acceleration vavg = (u + v) ÷ 2.
Instantaneous velocity
- Instantaneous velocity the velocity at one moment, equal to the gradient of the tangent on a displacement-time graph.
Average 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,
- which can have very different magnitudes.
Section 4 of 10Acceleration
1Acceleration
Acceleration the rate of change of velocity; it is a vector.
2a
Δv ÷ Δt = (v − u) ÷ 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)
- u is the initial velocity and v is the final velocity, so Δv = v − u.
3SI unit m s−2
- SI unit m s−2 it describes how much the velocity changes every second.
4Acceleration can come from changing speed, changing direction or both
- Acceleration can come from changing speed, changing direction or both a car at constant speed round a bend is accelerating.
Section 5 of 10Signs and slowing down
1State the positive direction first
- State the positive direction first and use signs consistently.
2
The sign of the acceleration is the sign of the change in velocity.
3
A trolley moving left and speeding up has increasingly negative velocity, so its acceleration is negative.
- A trolley moving left and slowing down has positive acceleration.
4An object decelerates when its acceleration is opposite to its velocity
- An object decelerates when its acceleration is opposite to its velocity this can be either sign.
5Zero velocity does not mean zero acceleration
- Zero velocity does not mean zero acceleration at the top of a throw v = 0 but a = −9.8 m s-2.
Section 6 of 10Uniform and non-uniform motion
Uniform and non-uniform motion
Uniform motion
Uniform motion constant velocity with zero acceleration.
Uniformly accelerated motion
Uniformly accelerated motion constant acceleration.
Free fall near the Earth's surface without air resistance
- Free fall near the Earth's surface without air resistance uniformly accelerated with g = 9.8 m s-2 downward.
In most real situations the acceleration changes
- In most real situations the acceleration changes use averages over an interval or instantaneous values from graphs.
The constant-acceleration equations
- The constant-acceleration equations must never be used across a stage where acceleration changes.
Section 7 of 10Measuring motion
Measuring motion
Two light gates a known distance apart
- Two light gates a known distance apart or a single gate with a card of known length, with a data logger calculating v = length ÷ time.
Acceleration follows from two velocities and the time between them.
Ticker-timers and motion sensors
- Ticker-timers and motion sensors give displacement against time directly.
Graphs of the data
- Graphs of the data give velocity and acceleration as gradients and areas.
Section 8 of 10More from the specification
More from the specification
Velocity-time graph interpretation
- The slope (gradient) of a velocity-time graph represents acceleration,
- while the area under a straight or curved line equals the change in displacement,
- which is a vector quantity.
Projectile motion components
- For a projectile launched horizontally from an initial height, horizontal motion occurs at constant horizontal velocity while vertical motion undergoes constant acceleration due to gravity.
- (a = g = 9.81 m s-2
Kinematics of free fall
- When a ball-bearing is dropped from rest through a measured height, its vertical displacement satisfies s = 1/2 g t2,
- allowing experimental determination of the acceleration of free fall g.
Vector vs scalar distinctions
- Displacement and velocity are vector quantities defined by both magnitude and direction,
- whereas distance and speed are scalar quantities describing only magnitude.
Velocity-time graph interpretation
- The slope (gradient) of a velocity-time graph represents acceleration,
- while the area under a straight or curved line equals the change in displacement,
- which is a vector quantity.
Projectile motion components
- For a projectile launched horizontally from an initial height, horizontal motion occurs at constant horizontal velocity while vertical motion undergoes constant acceleration due to gravity.
- (a = g = 9.81 m s-2
Kinematics of free fall
- When a ball-bearing is dropped from rest through a measured height, its vertical displacement satisfies s = 1/2 g t2,
- allowing experimental determination of the acceleration of free fall g.
Vector vs scalar distinctions
- Displacement and velocity are vector quantities defined by both magnitude and direction,
- whereas distance and speed are scalar quantities describing only magnitude.
Velocity-time graph interpretation
- The slope (gradient) of a velocity-time graph represents acceleration,
- while the area under a straight or curved line equals the change in displacement,
- which is a vector quantity.
Projectile motion components
- For a projectile launched horizontally from an initial height, horizontal motion occurs at constant horizontal velocity while vertical motion undergoes constant acceleration due to gravity.
- (a = g = 9.81 m s-2
Kinematics of free fall
- When a ball-bearing is dropped from rest through a measured height, its vertical displacement satisfies s = 1/2 g t2,
- allowing experimental determination of the acceleration of free fall g.
Vector vs scalar distinctions
- Displacement and velocity are vector quantities defined by both magnitude and direction,
- whereas distance and speed are scalar quantities describing only magnitude.
Velocity-time graph interpretation
- The slope (gradient) of a velocity-time graph represents acceleration,
- while the area under a straight or curved line equals the change in displacement,
- which is a vector quantity.
Projectile motion components
- For a projectile launched horizontally from an initial height, horizontal motion occurs at constant horizontal velocity while vertical motion undergoes constant acceleration due to gravity.
- (a = g = 9.81 m s-2
Kinematics of free fall
- When a ball-bearing is dropped from rest through a measured height, its vertical displacement satisfies s = 1/2 g t2,
- allowing experimental determination of the acceleration of free fall g.
Vector vs scalar distinctions
- Displacement and velocity are vector quantities defined by both magnitude and direction,
- whereas distance and speed are scalar quantities describing only magnitude.
Projectile
- Object moving under gravity alone in two dimensions.
Electromagnet
- Magnet made by current through a coil around a magnetic core.
Velocity-time graph
- A graph of velocity against time whose gradient is acceleration and area is displacement.
Kinematic equations
- Equations relating displacement, velocity, acceleration and time for constant acceleration.
Acceleration-time graph
- A graph of acceleration against time whose area is the change in velocity.
Projectile motion
- Two-dimensional motion with constant horizontal velocity and vertical acceleration g.
Vector quantity
- A quantity with both magnitude and direction.
Scalar quantity
- A quantity with magnitude only, such as potential
Section 9 of 10Key terms
| Term | Meaning |
|---|---|
| Distance | The total length of the path travelled; a scalar. |
| Displacement | The change in position of an object with its direction; a vector. |
| Speed | The rate of change of distance. |
| Velocity | The rate of change of displacement. |
| Acceleration | The rate of change of velocity. |
| Instantaneous velocity | The velocity at a single moment in time. |
| Uniform acceleration | Acceleration that stays constant. |
| Deceleration | Acceleration opposite to the direction of the velocity. |
Section 10 of 10Exam technique
1
Using distance instead of displacement when calculating velocity — check whether the direction reverses.
2
Thinking a negative acceleration always means slowing down — it depends on the sign of the velocity.
3
Assuming zero velocity means zero acceleration — at the top of a throw v = 0 but a = −9.8 m s-2.
4
Forgetting that changing direction at constant speed is an acceleration.
Marked practiceQuizzes for this lesson
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/s2downwards (air resistance negligible).