Question

The driver of a 2.0 × 103 kg red car traveling on the highway at 45m/s slams on his brakes to avoid striking a second yellow car in front of him, which had come to rest because of blocking ahead as shown in above Fig. After the brakes are applied, a constant friction force of 7.5 × 103 N acts on the car. Ignore air resistance.

Answer 1

Answer:

Newton's second law says:

7.5*10^3 = 2*10^3 * a

a = -7.5 /2 (negative) if distance moved is positive

v = Vi + a t = 45 - 7.5 t/2

when v = 0

7.5 t = 90

t = 12 seconds to stop

x = Vi t + (1/2) a t^2

x = 45*12 - 7.5/4 (144) = 540 - 270 = 270 meters to stop

now if x = 40

then

40 = 45 t - 7.5/4 t^2

1.875 t^2 - 45 t + 40 = 0

solve quadratic for t

then

v = 45 - (7.5/2) t