GCSE equations of motion Questions (higher only)
Equation
Comment
v = u + at
Acceleration is change in velocity ÷ time
s = ½ (v+u) × t Average velocity is ½ (v+u)
s = ut + ½ at²
No 'v' needed
v² - u² = 2as
No 't' needed
Don’t forget units too!
Speed (m/s)
Time (s)
Distance (m)
Acceleration (m/s2)
We often call these the suvat equations, with:
initial velocity u, final velocity v, acceleration a, displacement s, time t.
You will be given these in an exam
For the following equations, identify u, v, s, a and t, and solve.
1. A particle is accelerated uniformly from rest, so that after 10 seconds it has achieved a speed
of 15 m/s. Find its acceleration.
u=
v=
t=
equation to use:
a=
2. A car accelerates uniformly from rest and reaches 12m/s after covering 40m.. What is its
acceleration?
u=
v=
s=
equation to use:
a=
3. A car accelerates uniformly from 5m/s to 15m/s taking 7.5 seconds. How far did it travel
during this period?
u=
v=
t=
equation to use:
s=
4. A particle is accelerated from 1m/s to 5m/s over a distance of 15m. Find the acceleration.
u=
v=
s=
equation to use:
a=
5. A train starts from rest and accelerates uniformly at 1.5m/s2 until it attains a speed of 30m/s.
Find the time taken and the distance travelled.
u=
v=
a=
equation to use:
t=
s=
6. A train travels along a straight piece of track between 2 stations A and B. The train starts
from rest at A and accelerates at 1.25m/s2 until it reaches a speed of 20m/s. Find the distance
from A to B
u=
v=
a=
equation to use:
s=
7. A train is uniformly decelerated from 35m/s to 21m/s over a distance of 350m. Calculate the
deceleration.
u=
v=
s=
equation to use:
a=
Answers
1. A particle is accelerated uniformly from rest, so that after 10 seconds it has achieved a speed
of 15 m/s. Find its acceleration.
u = 0 m/s
v =15m/s
t = 10
equation to use: v = u + at
a= (v-u)÷t
a = (15-0)÷10 = 1.5m/s2
2. A car accelerates uniformly from rest and reaches 12m/s after covering 40m. What is its
acceleration?
u = 0m/s
v = 12m/s
s = 40m
equation to use: v² - u² = 2as
(v² - u²) ÷ (2 x s) = a
a = 122 ÷ (2x40) = 144 ÷ 80 = 1.8m/s2
3. A car accelerates uniformly from 5m/s to 15m/s taking 7.5 seconds. How far did it travel
during this period?
u = 5m/s
v = 15m/s
t = 7.5s
equation to use: s = ½ (v+u) × t
s = 0.5 (5+15) x 7.5 = 75m
4. A particle is accelerated from 1m/s to 5m/s over a distance of 15m. Find the acceleration.
u =1m/s
v =5m/s
s =15m
equation to use: v² - u² = 2as
(v² - u²) ÷ (2 x s) = a
a = (52 - 12) ÷ (2 x 15) = 24 ÷ 30 = 0.8 m/s2
5. A train starts from rest and accelerates uniformly at 1.5m/s2 until it attains a speed of 30m/s.
Find the time taken and the distance travelled.
u = 0m/s
v = 30m/s
a = 1.5m/s2
equation to use: v² - u² = 2as
(v² - u²) ÷ (2 x a) = s
s = 302 ÷ (2 x 1.5) = 900 ÷ 3 = 300m
v = u + at
t= (v-u)÷a
t = 30÷1.5= 20s
6. A train travels along a straight piece of track between 2 stations A and B. The train starts
from rest at A and accelerates at 1.25m/s2 until it reaches a speed of 20m/s. Find the distance
from A to B
u = 0m/s
v = 20m/s
a = 1.25m/s2
equation to use: v² - u² = 2as
(v² - u²) ÷ (2 x a) = s
s = 202 ÷ (2 x 1.25) = 160m
7. A train is uniformly decelerated from 35m/s to 21m/s over a distance of 350m. Calculate the
deceleration.
u = 35m/s
v = 21m/s
s = 350m
equation to use: v² - u² = 2as
(v² - u²) ÷ (2 x s) = a
a = (212 - 352) ÷ (2 x 350) = (441-1225)÷700 = -784÷700 = -1.12/s2