A particle moves along a line with x, v, and a representing position, velocity, and accele...

A particle moves along a line with x, v, and a representing position, velocity, and acceleration, respectively. Assuming that the acceleration a is constant, use equation (3.15) to show that

where x0 and v0 are the position and velocity of the particle at time t = 0, respectively. A car’s speed is reduced from 60mi/h to 30mi/h in a span covering 500 ft. Calculate the magnitude and direction of the constant deceleration.