Question

A 1500−kg car is driving toward the north along a straight horizontal road at a speed of 17.0 m/s. The driver applies the brakes and the car comes to a rest uniformly in a distance of 235 m. What are the magnitude and direction of the net force applied to the car to bring it to rest?

Answer 1

The magnitude of the net force required to stop the car is 1830 N, and the direction of the net force is toward the south because it opposes the car's initial northward motion.

Step-by-step explanation:

To find the magnitude and direction of the net force required to stop a 1500-kg car traveling north at a speed of 17.0 m/s over a distance of 235 m, we can use the work-energy principle or the kinematic equations along with Newton's second law of motion.

First, using the kinematic equation for uniformly accelerated motion:
v2 = u2 + 2as,
where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the stopping distance.

Given that the final velocity v is 0 (the car comes to a rest), we can solve for a:
0 = (17.0 m/s)2 + 2*a*235 m,
which gives us a = -1.22 m/s2. The negative sign indicates that the acceleration is in the opposite direction of the motion, which is to be expected since the car is braking.

Using Newton's second law, F = ma, we calculate the net force F:
F = (1500 kg)(-1.22 m/s2) = -1830 N.

The magnitude of the net force is 1830 N, and the direction is toward the south because it opposes the initial direction of motion, which is north.