AQA GCSE Equation of Motion(Physics)

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Uniform Acceleration

Uniform acceleration is when the acceleration is constant.

If an object has an acceleration of 5m/s2, then this means for every 1 second that passes the velocity will increase by 5m/s.

In this case the acceleration is uniform.

Equation of Motion

The following equation of motion can be used if the acceleration is uniform.

Equation of motion for final velocity squared- Initial velocity squared equals 2 x acceleration x distance

Example Calculations

1.A car has an initial velocity of 4m/s and travels over a distance of 50m, with a uniform acceleration of 2m/s2. Calculate the final velocity of the car.

V2-U2 = 2as

rearrange to make v the subject

v = ?, u = 4m/s, s = 50m, a = 2m/s2

2. A car accelerates from rest to a speed of 10m/s over a distance of 4m. Calculate the car’s acceleration

a = (v2-u2)/2s

a =?, V = 10m/s, U = 0m/s (at rest), s = 4m.

a = (102 – 02)/2×4

a = (100-0)/8

a = 100/8

a = 12.5m/s2

3.A man runs from rest with a uniform acceleration of 1m/s2 reaching a final velocity of 5m/s. Calculate the distance he travels to reach his final velocity.


s = (v2-u2)/2a

v = 5m/s, u = 0m/s (at rest), a = 1m/s2

s  = (52-02)/2 x1

s = 25/2

s = 12.5m

4.A motorbike reaches a velocity of 8m/s after accelerating at 2m/s2 over a distance of 12m. Calculate the initial velocity of the motorbike.

equation motion worked example to find initial velocity

Practice Question

1.A football is kicked from rest and accelerates to a maximum velocity of 3m/s over a distance of 5m. Calculate the acceleration of the football.

2. A train decreases its velocity from 25m/s to rest with an acceleration of -4m/s2. Calculate the distance travelled for the train to stop.

3. A cyclist reaches a velocity of 5m/s  after accelerating at 1m/s2 for a distance of 4m. Calculate the initial velocity of the cyclist.

4. A lion accelerates from rest to reach a final velocity, using an acceleration of 2m/s2 over a distance of 3m. Calculate the final velocity of the lion.

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