Answer to Question #157384 in Physics for Cecilia Knight

Question

A braking force of 6000 N was applied to a 1000-kg automobile bringing it to a complete stop in 75 m.

 

a. How much work was done in stopping the automobile?

 

b. How did the kinetic energy of the automobile change?

 

c. What relationship could be used to find the initial velocity of the automobile before the brakes were applied?

 

d. Calculate the initial velocity of the automobile before the brakes were applied.

Answer 1

a) $W=Fd=6000\ N\cdot75\ m=4.5\cdot10^5\ J.$

b)According to work-kinetic energy theorem:

$$\Delta KE=W=4.5\cdot10^5\ J.$$

c) The initial velocity of the automobile before the brakes were applied can be found trom the definition of the kinetic energy:

$$KE=\dfrac{1}{2}mv_i^2,$$ $$v_i=\sqrt{\dfrac{2KE}{m}}.$$

d) Let's calculate the initial velocity of the automobile before the brakes were applied:

$$v_i=\sqrt{\dfrac{2\cdot 4.5\cdot10^5\ J}{1000\ kg}}=30\ \dfrac{m}{s}.$$