Question

A car of mass 1200 kg is traveling at 2 m/s. Then it collides with a heavy boulder in the road. During the collision, the car moves forward only 15 cm before stopping. What is the average force exerted by the boulder on the car?

1.6 x 104 N
3.2 x 104 N
5.4 x 104 N
6.5 x 105 N
1.8 x 104 N

Answer 1

F = 1.6*10⁴ N

Step-by-step explanation:

Given distance x = 0.15m, mass m = 1200kg, velocity v = 2m/s.

Unknown: force F

Force is given by Newton's law:

(1)
`F = ma`

The average force to stop an object from a velocity will be the same force necessary to accelerate an object from rest to the same velocity.

The distance for an object starting from rest for a constant acceleration is given by:

(2)
`x=(1)/(2)at^2`

The velocity for an object starting from rest for a constant acceleration:

(3)
`v=at`

Using equation 2 and 3 to eliminate time t:

(4)
`x=(1)/(2)a(v^2)/(a^2)=(v^2)/(2a)`

Solving equation 4 for the acceleration a:

(5)
`a=(v^2)/(2x)`

Using equation1 to solve for the force F:

(6)
`F=ma=(mv^2)/(2x)`