Question

A girl operates a radio-controlled model car in a vacant parking lot. The girl’s position is at the origin of the xy coordinate axes, and the surface of the parking lot lies in the xy plane. She drives the car in a straight line so that the x coordinate is defined by the relation x(t) = 0.5t³ - 3t² + 3t + 2 where x and t are expressed in meters and seconds, respectively. Determine when the velocity is 0 m/s, and the position and the total distance travelled when the acceleration is zero.

Answer 1

The given equation for the position is, x(t)-05f -3r +3t+2 Derivate the above equation with respect to t for the velocity dt dt If the velocity is zero 1.5t2-6t+3-0 Solve above quadratic equation for t. t0.58 s (or)3.41s The position at t -0.58 sec is, x(0.58sec)-0.5(0.58sec)3(0.58sec)3(0.58sec) +2 - 2.82 m The position of the car, if the velocity is zero 1S 2.82m. Derivate the equation (2) for the acceleration, dv.(t) d dt dt If the acceleration is zero, a, (t)0 t2 sec The velocity of the car if the acceleration zero is v,(2)-15(2) - 6(2)+3 The distance travelled by the car if the acceleration zero is, dv(2)(-3 m/s)(2 s)--6 m =-3 m/s