Question

A motorcycle accelerates from 15 m/s to 20 m/s over a distance of 50 meters. What is its average acceleration?

Answer 1

Acceleration `= (7 )/(4) ms^-2 = 1.75 ms^-2`

Explanation:

Use the equation:

`s = (Deltav Deltat)/2 + v_0 Deltat`

Where `Deltav` is the change in velocity, so `Deltav=5ms^-1`
`v_0` is the initial speed, so `v_0=15ms^-1`
`Deltat` is the change in time, which is unknown.
s is the distance covered, s = 50m

Rearrange to make `Deltat` the subject:
`s = Deltat ((Deltav)/2 + v_0)`
`Deltat = s /((Deltav)/2 + v_0) = (50m) / (17.5ms^-1)=20/7 s`

Acceleration `= (Deltav)/(Deltat)`
Acceleration `= (5 ms^-1)/(20/7 s) = (5 ms^-1)*(7/20 s)`
Acceleration `= (7 )/(4) ms^-2 = 1.75 ms^-2`

Hint!
Rather than trying to remember:
`s = (Deltav Deltat)/2 + v_0 Deltat`
Visualise s as the area under a speed Vs time graph. Which for this case would look like this:
graph{1.75x + 15 [-0.5, 4, -5.12, 25]}