A vehicle is traveling in a linear path with a velocity of 20 m/s when a braking force decreases the speed at a rate of 21/(v+7) m/s2, where v is the velocity in m/s. Determine the stopping distance in meters Solution Note that a = v dv/dx = 21/(v + 7) Thus, v(v + 7)dv = 21dx Integrating, (v^3 / 3) + (7 v^2 / 2) = 21x + C At v = 20 m/s, x = 0, say. Thus, solving for C, C = 4066.67 Thus, (v^3 / 3) + (7 v^2 / 2) = 21x + 4066.67 Thus, solving for x when v = 0, xstop = 193.65 m [ANSWER].