AP TEST PROBLEM CAR AND MOTION EQUATION

A CAR OF MASS M MOVES WITH AN INITIAL SPEED Vo ON A STRAIGHT HORIZONTAL ROAD. THE CAR IS BROUGHT TO REST BY BRAKING IN SUCH A WAY THAT THE SPEED OF THE CAR IS GIVEN AS A FUNCTION OF TIME T BY

WHERE R IS A CONSTANT.

A) DEVELOP AN EQUATION THAT EXPRESSES THE TIME RATE OF CHANGE OF KINETIC ENERGY

B) DETERMINE THE TIME T IT TAKES TO BRING THE CAR TO A COMPLETE STOP

C) DEVELOP AN EQUATION FOR THE ACCELERATION OF THE CAR AS A FUNCTION OF TIME T.

D) ON THE AXES BELOW, SKETCH THE MAGNITUDE OF THE BRAKING FORCE AS A FUNCTION OF TIME T.