Newton's second law: A 1000-kg car is driving toward the north along a straight horizontal road at a speed of 20.0 m/s. The driver applies the brakes and the car comes to a rest uniformly in a distance of 200 m. What are the magnitude and direction of the net force applied to the car to bring it to rest?

Question

Quizplus · Accepted Answer

Using Newton's second law, we can find the net force applied to the car:
Fnet = ma
We know the mass is 1000 kg and the initial velocity is 20 m/s. To find the acceleration, we can use the kinematic equation:
v^2 = u^2 + 2as
where u = 20 m/s (initial velocity), v = 0 m/s (final velocity), s = 200 m (distance), and a is the acceleration.
Solving for a, we get:
a = (v^2 - u^2)/2s = (0 - 20^2)/(2*200) = -5 m/s^2 (the negative sign indicates that the acceleration is in the opposite direction of the initial velocity, i.e. south)
Substituting the values into the equation for net force:
Fnet = ma = 1000 kg * (-5 m/s^2) = -5000 N (also in the south direction)
However, the question asks for the magnitude of the net force (the absolute value), so we take the magnitude of -5000 N, which is 5000 N. Therefore, the magnitude and direction of the net force are:
Magnitude: 5000 N
Direction: south
The answer choice closest to this is C, with a value of 1.00 × 10^4 N (which is the same as 10000 N, rounded to two significant figures).

Newton's Second Law: a 1000-Kg Car Is Driving Toward the North