Question

A car starts from rest and travels for 5.0 seconds with a uniform acceleration of +1.5 m/s^2. The driver then applies the brakes, causing a uniform acceleration of -2.0 m/s^2. If the brakes are applied for 3.0 seconds, how fast is the car going at the end of the braking period, and how far has it gone from its start?

Answer 1

There are many ways to do this, some easy, some hard.

Momentum and impulse are conserved.

F*time=final momentum mv
but force=mass*acceleration

m*1.5m/s^2*5sec-m*2.0m/s^2*3sec=m(vf)

solve for Vf

Distance?
distance1=1/2 a t^2=1/2(1.5)5^2
distance2=vi*t-1/2 (2)3^2
where vi=at from the first or vi=1.5*5

so add the distances.

Answer 2

19.0