Calculating acceleration of a braking car.

Question

A 1.5 tonne car travelling at 100km/h suddenly brakes. The brakes provide an overall force of 50 times the normal reaction. Calculate the acceleration of the car.

Answer 1

Hi Caitlyn!

 

This question made me run for the internet to try to convert it into something I would see more normally in the United States. :)  With that in mind, I could recast the question as:

 

"A 1500 kg car traveling at 100 km/h suddenly brakes.  The brakes provide an overall force 50 times the normal force on the car.  Calculate the acceleration of the car."

 

Because there are no other vertical forces given for the car, we can pretty safely assume the only vertical forces are gravity and the normal force.  Since the car is not moving vertically, these two forces must be equal in magnitude (and opposite in direction).  So we have:

 

normal force = weight = (1500 kg)(9.8 m/s²)

 

Multiply that by 50 to get the friction force on the car.  We are also not told about any other significant horizontal forces on the car, besides friction.  So, in the horizontal, we have:

 

F_net = ma

 

where F_net is the force of friction.  You can solve for acceleration out of this equation.

 

Note that the speed the car is initially traveling makes no difference to the acceleration.  It would make a difference in how long in time and distance it takes the car to stop, but acceleration only depends on force, as per Newton's 2nd law.

 

I hope this helps you on your way.  If you have any more questions, or would like to check an answer, just let me know.