Physics 9702 · Paper 2

Displacement, Velocity & Acceleration

This chapter describes motion. It starts with the words: five quantities that say where something is and how it moves.
Three of them have definitions the exam asks for word for word: displacement, velocity and acceleration.

Distance and displacement

Distance is the length of the whole path an object travels, in metres.
is the distance moved in a stated direction: the straight line from start to finish, ignoring the path taken.
Walk 10 m north and then 10 m back south. The distance is 20 m, but the displacement is zero: you finished where you started.
Distance is a scalar and displacement is a vector. Lesson 1.8 covers scalars and vectors; here you only need the pairs.

A winding dashed walked path from A to B, with a straight arrow showing the direct displacement. — Distance is the length of the whole path walked; displacement is the straight line from start to finish.

Speed and velocity

Speed is distance travelled per unit time. It has no direction.
is the rate of change of displacement. It is the speed in a stated direction.

v = \dfrac{\Delta s}{\Delta t}

Symbols

$v$ = velocity (m s⁻¹)
$\Delta s$ = change in displacement (m)
$\Delta t$ = time taken (s)

Both cars move at the same speed (30 m s⁻¹, a scalar) but opposite velocities: velocity carries direction, speed does not.

A journey's speed usually changes, so $\Delta s / \Delta t$ over the whole journey gives the average velocity.
The velocity is the velocity at one moment. The next lesson shows how to read it from a graph.

Your turn— tap to reveal the worked answer (9702/21/M/J/24 Q2(a))

Define velocity. (9702/21/M/J/24 Q2(a))

Answer: velocity is the rate of change of displacement. “Speed in a given direction” is roughly right, but the mark scheme requires the rate-of-change wording, so learn it exactly.

Acceleration

is the rate of change of velocity: how much the velocity changes each second.

a = \dfrac{\Delta v}{\Delta t}

Symbols

$a$ = acceleration (m s⁻²)
$\Delta v$ = change in velocity (m s⁻¹)
$\Delta t$ = time taken (s)

Worked example

Warm-up: a train speeding up

A train's velocity increases from 4.0 m s⁻¹ to 10 m s⁻¹ in 3.0 s. Find its acceleration.

Change in velocity: $\Delta v = 10 - 4.0 = 6.0 \text{ m s}^{-1}$ .
$a = \dfrac{\Delta v}{\Delta t} = \dfrac{6.0}{3.0} = 2.0 \text{ m s}^{-2}$ .

Answer

a = 2.0 \text{ m s}^{-2}

Velocity is a vector, so acceleration is too. An object slowing down has an acceleration that points against its motion; with one chosen positive direction, that acceleration is negative. Slowing down is also called .
The three definitions repeat one pattern: rate of change. Velocity is the rate of change of displacement; acceleration is the rate of change of velocity.

Common mistake

On a define question, “how fast it moves” scores zero. The mark scheme accepts only the rate-of-change wording: “rate of change of displacement” for velocity, “rate of change of velocity” for acceleration.

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Displacement, Velocity & Acceleration

This chapter describes motion. It starts with the words: five quantities that say where something is and how it moves.
Three of them have definitions the exam asks for word for word: displacement, velocity and acceleration.

Distance and displacement

Distance is the length of the whole path an object travels, in metres.
is the distance moved in a stated direction: the straight line from start to finish, ignoring the path taken.
Walk 10 m north and then 10 m back south. The distance is 20 m, but the displacement is zero: you finished where you started.
Distance is a scalar and displacement is a vector. Lesson 1.8 covers scalars and vectors; here you only need the pairs.

Speed and velocity

Speed is distance travelled per unit time. It has no direction.
is the rate of change of displacement. It is the speed in a stated direction.

v = \dfrac{\Delta s}{\Delta t}

Symbols

$v$ = velocity (m s⁻¹)
$\Delta s$ = change in displacement (m)
$\Delta t$ = time taken (s)

Both cars move at the same speed (30 m s⁻¹, a scalar) but opposite velocities: velocity carries direction, speed does not.

A journey's speed usually changes, so $\Delta s / \Delta t$ over the whole journey gives the average velocity.
The velocity is the velocity at one moment. The next lesson shows how to read it from a graph.

Your turn— tap to reveal the worked answer (9702/21/M/J/24 Q2(a))

Define velocity. (9702/21/M/J/24 Q2(a))

Answer: velocity is the rate of change of displacement. “Speed in a given direction” is roughly right, but the mark scheme requires the rate-of-change wording, so learn it exactly.

Acceleration

is the rate of change of velocity: how much the velocity changes each second.

a = \dfrac{\Delta v}{\Delta t}

Symbols

$a$ = acceleration (m s⁻²)
$\Delta v$ = change in velocity (m s⁻¹)
$\Delta t$ = time taken (s)

Worked example

Warm-up: a train speeding up

A train's velocity increases from 4.0 m s⁻¹ to 10 m s⁻¹ in 3.0 s. Find its acceleration.

Change in velocity: $\Delta v = 10 - 4.0 = 6.0 \text{ m s}^{-1}$ .
$a = \dfrac{\Delta v}{\Delta t} = \dfrac{6.0}{3.0} = 2.0 \text{ m s}^{-2}$ .

Answer

a = 2.0 \text{ m s}^{-2}

Velocity is a vector, so acceleration is too. An object slowing down has an acceleration that points against its motion; with one chosen positive direction, that acceleration is negative. Slowing down is also called .
The three definitions repeat one pattern: rate of change. Velocity is the rate of change of displacement; acceleration is the rate of change of velocity.

Common mistake