Question

A 900 kg roller coaster car is travelling westward on the track and begins to slow down from 18m/s to 2m/s.

How long does it take the roller coaster car to decelerate if the force acting on the car to slow it is 7024N?

How far does the roller coaster travel during this time?

Answer 1

Use Newton's second law to determine the acceleration applied by the stopping force:

`F=ma\implies7024\,\mathrm N=(900\,\mathrm{kg})a\implies a\approx7.8\,(\rm m)/(\mathrm s^2)`

Then recall that

`{v_f}^2-{v_i}^2=2a\Delta x`

Take the direction in which the car is traveling to be positive, so that its acceleration points in the opposite direction and
`a` has negative sign. Then

`\left(2\,(\rm m)/(\rm s)\right)^2-\left(18\,(\rm m)/(\rm s)\right)^2=2\left(-7.8\,(\rm m)/(\mathrm s^2)\right)\Delta x\implies\Delta x\approx21\,\mathrm m`