A 14,700 N car is traveling at 25 m/s. The brakes are applied suddenly, and the car slides to a stop. The average braking force between the tires and the road is 7100 N. How far will the car slide once the brakes are applied?

Question

jamesj · Answer

Work-Energy theorem.  Look at your last questions and think about the change in KE.

anonymous · Answer

Work is the change in energy. Therefore, we can use the definition of work to find the distance the car will travel. First, we need to determine the amount of kinetic energy the vehicle has before brakes are applied. $$KE = {1 \over 2} m v^2$$We don't know the mass, but we do know the weight of the vehicle. Therefore, let's rewrite the kinetic energy as $$KE = {1 \over 2} {w \over g} v^2$$where $w$ is the weight of the vehicle. 

Now, we know that work is defined as $W = \Delta KE = \int {\bf F}dx$ Since the vehicle comes to a stop, we know the final kinetic energy will be zero, therefore the change in kinetic energy is equal to initial kinetic energy. Let's put all this together....$${1 \over 2} {w \over g} v^2 ={\bf F} x$$We can solve for x.