Which of these is a correct kinematic equation for constant acceleration?
Here is the subway train from the fourth kinematic equation again: in at 4 m/s, out at 10 m/s, 6 s elapsed. How far did it move in that stretch?
1. Write down the values in the question, and mark the unknown.
2. Write down the equation.
3. Substitute in the values.
A light-rail train slows steadily from 14 m/s to 6 m/s during 5 s. How far does it travel in that time?
Write down the values in the question:
v₀ = 14 m/s
v = 6 m/s
t = 5 s
Write down the equation:
Δx = ½(v₀ + v)t
Substitute in the values:
Δx = ½(14 + 6)(5)
Simplify:
Δx = ½(20)(5)
Δx = 50 m
A cyclist speeds up steadily from 5 m/s to 11 m/s during 3 s. How far does he travel in that time, in m? Enter the number only.
A car leaving a highway slows steadily from 18 m/s to 6 m/s during 5 s on the exit ramp. How far does it travel on the ramp, in m? Enter the number only.
When a different quantity is wanted, make it the subject first. For the time: divide both sides by ½(v₀ + v).
A boat speeds up steadily from 4 m/s to 14 m/s while covering 45 m. How long does that take?
Write down the values in the question:
Δx = 45 m
v₀ = 4 m/s
v = 14 m/s
Write down the equation:
Δx = ½(v₀ + v)t
Make t the subject:
t = 2Δx / (v₀ + v)
Substitute in the values:
t = (2 × 45) / (4 + 14)
Simplify:
t = 90 / 18
t = 5 s
A boat speeds up steadily from 7 m/s to 11 m/s while covering 36 m. How long does that take, in s? Enter the number only.
For one of the velocities: divide both sides by t and double, giving v₀ + v = 2Δx / t; then subtract the velocity you know.
Back to the subway train: in at 4 m/s, out at 10 m/s, 6 s elapsed. We now know it moved 42 m in that stretch — no acceleration required, because the average velocity carried the whole story.
A car speeds up steadily from 3 m/s to 13 m/s during 6 s. How far does it travel in that time, in m? Enter the number only.
A cart covers 40 m in 4 s while speeding up steadily from 6 m/s. What is its final velocity, in m/s? Enter the number only.
A delivery truck slows steadily from 22 m/s to 8 m/s while covering 75 m. How long does the slowdown take, in s? Enter the number only.