Answer to Question #143405 in Physics for Katrina

Question

A car is travelling along a highway at 108 km/h when the driver sees a caribou in the
road 50 m ahead. The driver applies the brakes which cause a 7500 N force to act on
the 1200 kg car.
a) Draw a free body diagram of the car.
b) What is the acceleration of the car when the brakes are applied?
c) How long does it take for the car to stop?
d) How far does the car travel while it is breaking?
e) Does the car hit the caribou?

Answer 1

a) It is below:

b) The acceleration is (according to Newton's second law)

$$a=\frac Fm=\frac{7500}{1200}=6.25\text{ m/s}^2.$$

c) From the speed of 108 km/h, which is

$$v=108\cdot1000/3600=30\text{ m/s},$$

this will take a time of

$$t=\frac{v_f-v_i}{a}=\frac{30-0}{6.25}=4.8\text{ s}.$$

d) The braking distance is

$$d=\frac{v^2_f-v^2_i}{2a}=72\text{ m}.$$

e) Unfortunately, yes.