A car starts from rest and accelerates uniformly at the rate of $ 10 cms^{-2} $ and reaches a maximum velocity of $72 kmph$. it travels with this maximum velocity for some time and retards uniformly at the rate of $ 20 cms^{-2} $ and comes to a stop. if the total distance covered by the body is $ 5 km$, find the total time of travel of the body in sec

Convert units: 72 km/h = 20 m/s. Acceleration = 0.1 m/s^2, Retardation = 0.2 m/s^2. Time to reach max velocity: t1 = 20 / 0.1 = 200 s. Distance during acceleration: d1 = 0.5 * 0.1 * 200^2 = 2000 m. Time to stop: t3 = 20 / 0.2 = 100 s. Distance during retardation: d3 = 0.5 * 0.2 * 100^2 = 1000 m. Remaining distance = 5000 - 2000 - 1000 = 2000 m. Time at constant velocity: t2 = 2000 / 20 = 100 s. Total time = 200 + 100 + 100 = 400 s.