A bus speeds up from 5 m/s to 17 m/s in 6 s. What is its acceleration, in m/s²?
Here is the same kind of car problem, turned around.
A car pulls away at 4 m/s and accelerates at 3 m/s². How long until it reaches 16 m/s? This time the unknown isn't v — it's t. And in v = v₀ + at, the t sits inside the product at.
The equation still links the four values: v = v₀ + at. To find t, rearrange the equation until t stands alone — until t is the 'subject' of the equation: the quantity standing alone on one side of the equals sign, the thing the equation gives you directly.
Take v₀ from both sides. Then divide both sides by a.
Now solve the question with the same steps as always — with one extra step for the rearranging.
1. Write down the values in the question, and mark the unknown.
A car accelerates at 3 m/s² from 5 m/s to 23 m/s. How long does the change take?
Write down the values in the question:
v₀ = 5 m/s
v = 23 m/s
a = 3 m/s²
Write down the equation:
v = v₀ + at
Make t the subject:
t = (v − v₀) / a
Substitute in the values:
t = (23 − 5) / 3
Simplify:
t = 18 / 3
t = 6 s
A motorcycle accelerates at 4 m/s² from 6 m/s to 26 m/s. How long does the change take, in s? Enter the number only.
Sometimes the unknown is a: a question gives the two velocities and the time, and asks for the acceleration. The same two moves work.
A speedboat goes from 4 m/s to 19 m/s in 5 s. What is its acceleration?
Write down the values in the question:
v₀ = 4 m/s
v = 19 m/s
t = 5 s
Write down the equation:
v = v₀ + at
Make a the subject:
a = (v − v₀) / t
Substitute in the values:
a = (19 − 4) / 5
Simplify:
a = 15 / 5
a = 3 m/s²
A car goes from 8 m/s to 32 m/s in 6 s. What is its acceleration, in m/s²? Enter the number only.
A bus slows from 24 m/s to 6 m/s while braking at −3 m/s². How long does the slowdown take, in s? Enter the number only.
Back to the car at the start: it pulled away at 4 m/s with an acceleration of 3 m/s². We now know it reached 16 m/s exactly 4 s after pulling away — and we could work that time out without ever having to run a stopwatch.
A train slows from 30 m/s to 12 m/s in 6 s. What is its acceleration, in m/s²? Include the sign in your answer.
A race car accelerates at 8 m/s² from 7 m/s to 39 m/s. How long does the change take, in s? Enter the number only.
A car slows from 18 m/s to 4 m/s in 4 s. What is its acceleration, in m/s²? Include the sign in your answer.