Distance, displacement, speed, velocity and acceleration

A-Level Physics· Unit 2: Kinematics, 2.1 Kinematics· 20 min read

1. Distance and Displacement: Scalars vs Vectors★☆☆☆☆⏱ 5 min

📘 Definition

Scalar vs Vector Quantities

Scalars are quantities described only by magnitude (size). Vectors require both magnitude and direction to be fully defined. Distance and displacement are the two core quantities describing an object's position change.

Example:

Distance ( $d$ ) = 5 m (scalar, no direction needed), Displacement ( $s$ ) = 5 m north (vector, direction required)

Distance measures the total length of the path an object has travelled between two points. Displacement measures the straight-line net change in position from the object's starting point to its end point.

📐 Worked Example

A runner completes one full lap of a 400 m circular running track, ending at the same point they started. Find the runner's distance travelled and displacement.

1
Distance is the total length of the path travelled. One lap is 400 m, so:
2
$d = 400 \text{ m}$
3
Displacement is the net change in position from the start point. Since the runner ends at the same point they started, the change in position is:
4
$s = 0 \text{ m}$

Exam tip:

Always state the direction of any vector quantity in your answer to get full marks.

2. Speed and Velocity★★☆☆☆⏱ 7 min

📘 Definition

Speed vs Velocity

Average speed: $v_{a v} = \frac{total distance}{total time}$ , Average velocity: $v_{a v} = \frac{total displacement}{total time}$

Speed is the rate of change of distance (scalar). Velocity is the rate of change of displacement (vector). Average values are calculated over a time interval, while instantaneous values are measured at a single moment in time.

Because velocity depends on displacement, a change in direction will change velocity even if speed remains constant. This is an extremely common exam point.

📐 Worked Example

A car travels 10 km north in 15 minutes, then travels 6 km south in 10 minutes. Calculate the car's average speed and average velocity.

1
Convert all quantities to SI units: total distance = 10 km + 6 km = 16 km = 16000 m, total time = 15 min + 10 min = 25 min = 1500 s
2
Calculate average speed:
3
$v_{speed, av} = \frac{16000}{1500} \approx 10.7 \text{ m s}^{-1}$
4
Calculate net displacement, taking north as positive: net displacement = +10 km - 6 km = +4 km = 4000 m (north)
5
Calculate average velocity:
6
$v_{av} = \frac{4000}{1500} \approx 2.67 \text{ m s}^{-1} \text{ north}$

3. Acceleration★★☆☆☆⏱ 6 min

📘 Definition

Acceleration

a = \frac{\Delta v}{\Delta t} = \frac{v - u}{t}, where $u$ = initial velocity, $v$ = final velocity, $Δ t$ = time interval

Acceleration is defined as the rate of change of velocity. It is a vector quantity, meaning its sign and magnitude depend on the direction of velocity change.

Acceleration occurs whenever velocity changes: this can be speeding up, slowing down, or changing direction. A negative acceleration (often called deceleration) just means acceleration points in the opposite direction to the chosen positive direction.

📐 Worked Example

A cyclist accelerates from rest to 12 m s⁻¹ in 4.0 s, moving in a straight line east. Taking east as the positive direction, calculate the cyclist's acceleration.

1
Identify initial and final velocity: $u = 0 m s^{- 1}$ , $v = + 12 m s^{- 1}$ , $t = 4.0 s$
2
Substitute into the acceleration formula:
3
$a = \frac{v - u}{t} = \frac{12 - 0}{4.0} = 3.0 \text{ m s}^{-2}$
4
State the direction: acceleration is $3.0 m s^{- 2}$ east

4. Common Pitfalls

Wrong move:

Assuming distance is always equal to the magnitude of displacement

Why:

Distance is total path length, while displacement is net position change. They only equal for straight-line motion with no direction change.

Correct move:

Always check if the object changes direction when comparing distance and displacement.

Wrong move:

Calculating average velocity as the average of individual velocities

Why:

Average velocity is defined as total displacement divided by total time, not the average of separate velocities.

Correct move:

Always calculate total displacement first, then divide by total elapsed time.

Wrong move:

Assuming negative acceleration always means the object is slowing down

Why:

Negative acceleration only means acceleration points opposite to your chosen positive direction. If velocity is also negative, negative acceleration means the object is speeding up.

Correct move:

Always define your positive direction first, then compare the signs of acceleration and velocity to see if the object speeds up or slows down.

Wrong move:

Claiming acceleration is zero if speed is constant

Why:

Acceleration depends on change in velocity, not speed. Velocity changes if direction changes, even if speed is constant.

Correct move:

Always check for direction changes when determining if acceleration is zero.

5. Quick Reference Cheatsheet

Quantity	Type (Scalar/Vector)	Definition	SI Unit
Distance	Scalar	Total path length travelled	m
Displacement	Vector	Net change in position from start	m
Speed	Scalar	Rate of change of distance	m s⁻¹
Velocity	Vector	Rate of change of displacement	m s⁻¹
Acceleration	Vector	Rate of change of velocity	m s⁻²

When this came up on past exams

AI-estimated based on syllabus patterns — cross-check with official past papers for accuracy. Use only as revision-focus signals.

2023 · 1
Distinguish displacement vs distance
2022 · 2
Calculate average velocity
2021 · 1
Acceleration for direction change

Going deeper

syllabusCIE 9702 2025-2027 Syllabus

What's Next

Mastering the definitions of these core kinematic quantities is critical for all further work on motion. Confusion between scalar and vector properties is one of the most common sources of lost marks in CIE exams, so take time to confirm you can distinguish each pair. Next, you will learn how to represent motion graphically with displacement-time and velocity-time graphs, then use these to derive the kinematic equations for constant acceleration that you will use for almost all straight-line motion problems.