Question

A car driver has rear ended a truck but claims he was driving the speed limit before hitting the brakes. The driver left a 50m long streak of tire rubber when he slammed on the brakes. The mass of the drivers car is 1000kg. The coefficient of friction between the tire and asphalt is 0.5. The mass of the truck that got hit is 5000kg. The speed limit for the road is 40mph. What was the magnitude of the acceleration of the car? (Remember that magnitudes are always positive). How fast was the car going right before the driver slammed on the brakes?

Answer 1

In the below figure it is shown the physics situation.

We put the reference frame in the point where the car driver hit the brake. The x axis points to the right and the y axis point upwards.

Drawing the free-body diagram of the car and using Newton's second law we obtain:

in the x axis, and

in the y axis.

From the equation one we have:

.

But the kinetic friction force is given by:

.

From the equation two we obtain , therefore:

.

Replacing the kinectic friction force in the equation 3 we obtain:

Therefore, the magnitude of the acceleration is

.

For an object with motion with constant acceleration we have:

, where is the final speed, is the initial speed, is the acceleration of

the car and is the displacement of the car.

Isolating the initial speed we obtain:

.

But .

The car driver exceeded the the maximun speed limit for the road.