Velocity and Acceleration: KS3 Physics Explained

Predict first: if a car drives north at 20 m/s then turns east at 20 m/s, has its velocity changed? Yes — direction changed. Velocity is displacement divided by time (a vector), speed is distance divided by time (a scalar), and acceleration is the rate at which velocity changes. All three distinctions are essential KS3 physics.

What is the difference between speed and velocity?

Speed and velocity both measure how fast an object moves, but they are fundamentally different types of quantity:

Property | Speed | Velocity
Type | Scalar — magnitude only | Vector — magnitude and direction
Formula | speed = distance ÷ time | velocity = displacement ÷ time
Unit | m/s | m/s (with a direction stated)
Example | 30 m/s | 30 m/s due north

Displacement is the straight-line distance from start to finish, measured in a specific direction — it is not the same as total distance travelled. A runner who completes one lap of a 400 m track has covered 400 m but has a displacement of zero (they are back where they started).

Predict first: A car travels 50 km east, then 50 km west, returning to its starting point. What is the total distance? What is the displacement? Total distance = 100 km; displacement = 0 km.

What is acceleration?

Acceleration is the rate of change of velocity over time. Since velocity is a vector, acceleration is also a vector — it has both magnitude and direction.

The formula is:

a = (v − u) ÷ t

Where:

a = acceleration (m/s²)

v = final velocity (m/s)

u = initial velocity (m/s)

t = time taken (s)

A positive value of a means the object is speeding up (in the direction of motion). A negative value (sometimes called deceleration) means the object is slowing down.

How do you calculate velocity?

Velocity is calculated by dividing displacement by time:

velocity (m/s) = displacement (m) ÷ time (s)

Worked example:

A cyclist travels 240 m due north in 30 seconds. What is their velocity?

Displacement = 240 m (north)

Time = 30 s

velocity = 240 ÷ 30 = 8 m/s north

Note that if the question asked for speed and gave total distance (rather than displacement), the method is identical but you do not state a direction.

How do you calculate acceleration?

Use the formula a = (v − u) ÷ t and substitute the values carefully.

Worked example 1 — speeding up:

A train starts from rest (u = 0 m/s) and reaches a velocity of 25 m/s in 50 seconds. What is its acceleration?

v = 25 m/s, u = 0 m/s, t = 50 s

a = (25 − 0) ÷ 50 = 0.5 m/s²

Worked example 2 — slowing down:

A car travelling at 18 m/s brakes to a standstill in 6 seconds. What is its acceleration?

v = 0 m/s, u = 18 m/s, t = 6 s

a = (0 − 18) ÷ 6 = −3 m/s²

The negative sign shows the car is decelerating. A deceleration of 3 m/s² means the car loses 3 m/s of velocity every second.

What do distance-time and velocity-time graphs show?

Feature | Distance-time graph | Velocity-time graph
y-axis | Distance (m) | Velocity (m/s)
x-axis | Time (s) | Time (s)
Horizontal line | Object stationary | Constant velocity (zero acceleration)
Straight sloping line | Constant speed | Constant acceleration
Curved line (steepening) | Increasing speed (acceleration) | Increasing acceleration
Gradient of the line | Speed (m/s) | Acceleration (m/s²)
Area under the line | Not directly useful | Distance (displacement) travelled

Key rule for distance-time graphs: gradient = speed. Pick two points on the straight line, read off Δdistance and Δtime, and divide.

Key rule for velocity-time graphs: gradient = acceleration; area under line = distance.

What does a curved distance-time graph tell you?

A straight line on a distance-time graph shows constant speed — equal distances in equal time intervals. A curved line (getting steeper) tells you the speed is increasing: the object is covering more distance each second than it did in the previous second. That increase in speed over time is, by definition, acceleration.

To find the speed at a particular instant from a curve, you draw a tangent to the curve at that point and calculate the gradient of that tangent line. This is a technique you will practise more formally at GCSE.

A curve that flattens (becomes less steep) means the object is slowing down — decelerating — and will eventually become a horizontal line if the object stops.

Frequently asked questions

What is the formula for velocity?

Velocity = displacement ÷ time, or v = s ÷ t, where s is displacement in metres and t is time in seconds. The result is in m/s and must always include a direction to be a true velocity (e.g. 10 m/s north). If direction is not specified, you are calculating speed rather than velocity.

What is the formula for acceleration in KS3 physics?

Acceleration = change in velocity ÷ time taken, written as a = (v − u) ÷ t. Here v is the final velocity, u is the initial velocity, and t is the time for that change. The unit is metres per second squared (m/s²). A positive answer means speeding up; a negative answer means slowing down (decelerating).

Can an object accelerate without changing its speed?

Yes. Because velocity is a vector (it includes direction), any change in direction is a change in velocity — even if speed stays constant. A car moving at 20 m/s around a roundabout is constantly changing direction, so it is constantly changing velocity, so it is accelerating. This is called centripetal acceleration and you will study it in more depth at GCSE and A-level.

How do you find acceleration from a velocity-time graph?

The acceleration equals the gradient (slope) of the velocity-time graph. Choose two clear points on the straight line, read their coordinates, and calculate: a = (v₂ − v₁) ÷ (t₂ − t₁). A steeper gradient means greater acceleration. A negative gradient indicates deceleration. A horizontal line has a gradient of zero, meaning zero acceleration and constant velocity.

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