Answer to Question #268497 in Physics for Andy

Question

1. Mrs. Salcedo's car of mass 2.4 x 10³ kg travelling on the highway when the teacher receives an emergency call. She increased the speed of the car to 33 m/s.The increase in speed results in 3.1 x10^5 J of work done on the car. Determine the initial speed of the car in km/h.

Answer 1

We can find the initial speed of the car from the work-kinetic energy theorem:

$$W=\Delta KE=KE_f-KE_i,$$ $$W=\dfrac{1}{2}mv_f^2-\dfrac{1}{2}mv_i^2,$$ $$v_i=\sqrt{\dfrac{2(\dfrac{1}{2}mv_f^2-W)}{m}},$$ $$v_i=\sqrt{\dfrac{2\times(\dfrac{1}{2}\times2.4\times10^3\ kg\times(33\ \dfrac{m}{s})^2-3.1\times10^5\ J)}{2.4\times10^3\ kg}},$$ $$v_i=28.8\ \dfrac{m}{s}\times\dfrac{1\ km}{1000\ m}\times\dfrac{3600\ s}{1\ h}=104\ \dfrac{km}{h}.$$