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    Speed, velocity and acceleration: worked questions

    By Engr. Mehmood Kakar · Updated

    Quick answer

    Speed is how fast something moves (distance ÷ time); velocity is speed in a given direction; acceleration is the change in velocity ÷ time taken, a = Δv ÷ t. On a distance–time graph the gradient is the speed. On a velocity–time graph the gradient is the acceleration and the area underneath is the distance travelled.

    Speed vs velocity

    Speed is a scalar: just a size. Velocity is a vector: a size and a direction. That matters whenever the direction changes. A car going round a roundabout at a steady 10 m/s has a constant speed, but its velocity keeps changing because its direction does, so it is accelerating.

    Speed: s = vt

    AQA writes this as distance travelled = speed × time, s = v t. Use metres and seconds for an answer in m/s.

    A cyclist travels 1.2 km in 4 minutes. Calculate their average speed in m/s.

    1. Convert: s = 1.2 km = 1200 m, t = 4 × 60 = 240 s
    2. Rearrange: v = s ÷ t
    3. v = 1200 ÷ 240
    4. v = 5.0 m/s

    A train moves at 30 m/s for 2.5 minutes. How far does it travel?

    1. Convert: t = 2.5 × 60 = 150 s
    2. s = v × t = 30 × 150
    3. s = 4500 m (4.5 km)

    Typical speeds

    You are expected to know rough values like these, which can be used in estimate questions:

    Moving thingTypical speed
    Walkingabout 1.5 m/s
    Runningabout 3 m/s
    Cyclingabout 6 m/s
    Sound in airabout 330 m/s

    Car and train speeds vary a lot with the road or track, so questions usually give them.

    Acceleration: a = Δv/t

    Acceleration is the change in velocity divided by the time it takes: a = Δv ÷ t, where Δv = final velocity − initial velocity. The unit is m/s².

    A car speeds up from rest to 24 m/s in 8.0 s. Calculate its acceleration.

    1. Δv = 24 − 0 = 24 m/s
    2. a = Δv ÷ t = 24 ÷ 8.0
    3. a = 3.0 m/s²

    A bus slows from 20 m/s to 5.0 m/s in 5.0 s. Calculate its acceleration.

    1. Δv = 5.0 − 20 = −15 m/s
    2. a = Δv ÷ t = −15 ÷ 5.0
    3. a = −3.0 m/s² (a deceleration of 3.0 m/s²)

    An object falling freely near the Earth’s surface accelerates at about 9.8 m/s². If a question gives distances instead of time, use v² − u² = 2as.

    Distance–time graphs

    • Gradient = speed. A steeper line means a faster object.
    • Horizontal line: stationary.
    • Straight sloping line: constant speed.
    • Curve getting steeper: speeding up. For the speed at one moment, draw a tangent and find its gradient (Higher).

    A straight line on a distance–time graph goes from (0 s, 0 m) to (20 s, 100 m). Find the speed.

    1. gradient = change in distance ÷ change in time = 100 ÷ 20
    2. speed = 5.0 m/s

    Velocity–time graphs

    • Gradient = acceleration. A negative gradient means slowing down.
    • Horizontal line: constant velocity (zero acceleration).
    • Area under the line = distance travelled (Higher on AQA).

    A car accelerates steadily from rest to 24 m/s in 8.0 s, then travels at 24 m/s for 10 s. How far does it go in total?

    1. Triangle (accelerating): area = ½ × 8.0 × 24 = 96 m
    2. Rectangle (steady speed): area = 10 × 24 = 240 m
    3. Total distance = 96 + 240 = 336 m

    Common mistakes

    • Final minus initial the wrong way round. Δv = v − u. Slowing down gives a negative answer.
    • Leaving time in minutes or distance in km. Convert to seconds and metres.
    • Reading the wrong graph. The gradient of a distance–time graph is speed; the gradient of a velocity–time graph is acceleration.
    • Wrong unit for acceleration. It is m/s², not m/s.

    Practice

    1. A runner covers 400 m in 80 s. What is their average speed?

    v = s ÷ t = 400 ÷ 80 → v = 5.0 m/s

    2. A rocket goes from 0 to 150 m/s in 6.0 s. Calculate its acceleration.

    a = Δv ÷ t = 150 ÷ 6.0 → a = 25 m/s²

    3. A car accelerates at 2.0 m/s² for 7.5 s from 5.0 m/s. What is its final velocity?

    Δv = a × t = 2.0 × 7.5 = 15 m/s → v = 5.0 + 15 → v = 20 m/s

    4. A velocity–time graph shows a cyclist slowing steadily from 6.0 m/s to rest in 4.0 s. How far do they travel while stopping?

    Area of triangle = ½ × 4.0 × 6.0 → distance = 12 m

    Frequently asked questions

    What is the difference between speed and velocity?

    Speed is a scalar: it only has a size, such as 20 m/s. Velocity is a vector: it has a size and a direction, such as 20 m/s north. Two cars at 20 m/s going opposite ways have the same speed but different velocities.

    What is the equation for acceleration?

    Acceleration = change in velocity ÷ time taken, a = Δv ÷ t, where Δv = final velocity − initial velocity. Acceleration is measured in metres per second squared (m/s²).

    What does a negative acceleration mean?

    The object is slowing down (decelerating), if it is moving in the positive direction. For example, a car going from 20 m/s to 5 m/s in 5 s has an acceleration of −3 m/s².

    How do you find distance from a velocity–time graph?

    Work out the area under the line. Split it into rectangles and triangles if needed, and use the units on the axes. For a curved line, count squares and multiply by the distance each square represents. This is Higher tier on AQA.

    Can an object have a constant speed but a changing velocity?

    Yes. An object moving in a circle at a steady speed keeps changing direction, so its velocity keeps changing and it is accelerating.

    Engr. Mehmood Kakar

    Written by Engr. Mehmood Kakar

    Physics educator and engineer (MSc Physics, B.Ed, M.Ed) with 8 years of hands-on teaching, from college students to teacher training. About the author · LinkedIn (opens in a new tab)

    Checked against the AQA GCSE Physics (8463) specification on 15 November 2026.