Question

QUESTION 7

How much force is required to bring a car of mass 1,126 kg, initially traveling at 20.4 m/s, to rest in 7.4 s?

Answer 1

The force required is 3,104 N

Step-by-step explanation:

Force

According to the second Newton's law, the net force exerted by an external agent on an object of mass m is:

F = ma

Where a is the acceleration of the object.

On the other hand, the equations of the Kinematics describe the motion of the object by the equation:

`v_f=v_o+at`

Where:

vf is the final speed

vo is the initial speed

a is the acceleration

t is the time

Solving for a:

`\displaystyle a=(v_f-v_o)/(t)`

We are given the initial speed as vo=20.4 m/s, the final speed as vf=0 (at rest), and the time taken to stop the car as t=7.4 s. The acceleration is:

`\displaystyle a=(0-20.4)/(7.4)`

`a=-2.757\ m/s^2`

The acceleration is negative because the car is braking (losing speed). Now compute the force exerted on the car of mass m=1,126 kg:

`F = 1,126\ kg * 2.757\ m/s^2`

F= 3,104 N

The force required is 3,104 N