A cyclist moving at 4 m/s accelerates at 1.5 m/s² while covering 35 m. What is her final speed, in m/s? Enter the number only.
Here is a motorcycle speeding up from 6 m/s to 18 m/s over 36 m of road.
Nothing timed the motorcycle's run from 6 m/s to 18 m/s over those 36 m. What acceleration did that take? The equation v² = v₀² + 2aΔx links these values — but the unknown is a, and it sits inside the term 2aΔx. To find it, we need to rearrange.
Two moves free a: take v₀² from both sides, then divide both sides by 2Δx.
Now the motorcycle, with the same steps as always.
1. Write down the values in the question, and mark the unknown.
4. Substitute in the values, and simplify. Square the velocities first — 18² = 324 and 6² = 36 — and subtract them in this order: final squared minus starting squared.
A scooter speeds up from 5 m/s to 13 m/s over 24 m. What is its acceleration, in m/s²? Enter the number only.
Sometimes the distance is the unknown: a question gives the two velocities and the acceleration, and asks how much road the change took. The same two moves work.
A car slows from 15 m/s to 3 m/s with an acceleration of −4 m/s². How much road does the slowdown take?
Write down the values in the question:
v₀ = 15 m/s
v = 3 m/s
a = −4 m/s²
Write down the equation:
v² = v₀² + 2aΔx
Make Δx the subject:
Δx = (v² − v₀²) / 2a
Square both velocities:
3² = 9, 15² = 225
Substitute in the values, and calculate:
Δx = (9 − 225) / (2 × (−4))
Δx = (−216) / (−8)
Δx = 27 m
The negative velocity-squared change and the negative acceleration cancel, and a positive length of road comes out.
A jet ski speeds up from 4 m/s to 16 m/s with a constant acceleration of 6 m/s². How far does it travel during the change, in m? Enter the number only.
A car slows from 26 m/s to 14 m/s over 48 m. What is its acceleration, in m/s²? Include the sign in your answer.
Back to the motorcycle: it went from 6 m/s to 18 m/s over 36 m of road. We now know its acceleration was 4 m/s² — and nothing ever needed a stopwatch.
A sedan speeds up from 8 m/s to 20 m/s over 28 m while overtaking. What is its acceleration, in m/s²? Enter the number only.
A car slows from 26 m/s to 10 m/s with a constant acceleration of −6 m/s². How much road does the slowdown take, in m? Enter the number only.
A van speeds up from 12 m/s to 18 m/s over 25 m. What is its acceleration, in m/s²? Enter the number only.