intial and final velocity (pls help)

Question

While driving on highway 401 you see a traffic jam ahead. Not wanting to apply the brake, you take your foot off the gas and let the car slow down on its own. Your acceleration is -4.0 m/s² (remember you are slowing down) and the mass of the car is 1 200 kg.

a) How much frictional force acted to slow down the car?   

b) While slowing down, the car travels 85 m in 3.2 s. What was your initial velocity?

c) What was your final velocity?

Answer 1

We will need to use 3 equations;

1)     We can use D = Vo x t + ½ x a x t^2. We know D, t, and a, so we can solve for Vo. Making the required substitutions, we get Vo = 33 m/s.

2)    As we now know the initial velocity, we can calculate the final velocity using

Vf^2 = Vo^2 + 2 x a x D where D is the distance.

Vf^2 = 33.0^2 m/s - 2 x 4.0 m/s^2 x 85 m/s   Solve for Vf.

Vf = 20.2 m/s

3)     The difference in initial and final kinetic energy must be equal to work done by the frictional force.

The force required to stop the car can be found from ΔKE = Fr x D. As we can calculate the initial and final KE, and know the stopping distance, D, we can solve for Fr.

½ M x Vo^2 – ½ x M Vf^2 = 85 x Fr

Fr = ½ x M x (Vo^2 – Vf^2) / 85

This gives Fr = 4087 Newtons.

Please check math.