A 1000-kg car is driving toward the north along a straight horizontal road at a speed of .The driver applies the brakes and the car comes to a rest uniformly in a distance of .What are the magnitude and direction of the net force applied to the car to bring it to rest?

Question

A 1000-kg car is driving toward the north along a straight horizontal road at a speed of  .The driver applies the brakes and the car comes to a rest uniformly in a distance of  .What are the magnitude and direction of the net force applied to the car to bring it to rest?

Quizplus · Accepted Answer

First, we need to find the initial kinetic energy of the car:
K_i = (1/2)mv_i^2 = (1/2)(1000 kg)(11 m/s)^2 = 605,000 J

Next, we need to find the average net force applied to the car during braking:
F_net = ma_avg

We can find the average acceleration using the distance and initial velocity:
d = (1/2)at^2 + v_it
0 = (1/2)at^2 + (11 m/s)t - 70 m
Solving for t using the quadratic formula:
t = 6.34 s

a_avg = (v_f - v_i) / t
a_avg = (0 - 11 m/s) / 6.34 s
a_avg = -1.74 m/s^2

Now we can find the net force:
F_net = (1000 kg)(-1.74 m/s^2) = -1.74 × 10^3 N

Since the force is acting in the opposite direction of the initial motion, the direction of the net force is south. The magnitude of the net force is 1.74 × 10^3 N, which is closest to 1.00 × 10^3 N, which is answer choice C.

A 1000-Kg Car Is Driving Toward the North Along a Straight