Question

A 500 kg car is moving at 30 m/s. The driver sees a barrier ahead. If the car takes 100 m to come to rest, what is the magnitude of the force necessary to stop the car?
How do you solve this question?

Answer 1

Answer:

F = 2250 [N]

Explanation:

In order to solve this problem, we must first use the following equation of kinematics.

$v_{f}^{2} =v_{o}^{2}-2*a*x$

where:

Vf = final velocity = 0 (come to rest)

Vo =  initial velocity = 30 [m/s]

a = acceleration or desaceleration [m/s²]

x = distance = 100 [m]

$(0)=30^{2} -2*a*100\\900 = 200*a\\a = 4.5 [m/s^{2}]$

Now we must use the following equation of kinetics, which is based on Newton's second law that explains that the sum of forces on a body is equal to the product of mass by acceleration.

∑F = m*a

where:

F = force [N]

m = mass = 500 [kg]

a = acceleration = 4.5 [m/s²]

$F = 500*4.5\\F = 2250 [N]$