A car starting from rest accelerates at the rate f through a distance S , then continues at a constant speed for time t and then decelerates at rate f /2 to come to rest. If the total distance travelled is 15 S , then

Step-by-step solution

The velocity-time graph for the given situation can be drawn as below. Magnitudes of slope of O A = f And slope of B C = f 2 v = f t 1 = f 2 t 2 t 2 = 2 t 1 In graph area of ∆ O A D gives Distance, S = 1 2 f t 1 2 … . i Area of rectangle A B E D gives distance travelled in time t . S 2 = f t 1 t Distance travelled in time t 2 = S 3 = 1 2 f 2 2 t 1 2 Thus, S 1 + S 2 + S 3 = 15 S S + f t 1 t + f t 1 2 = 15 S S + f t 1 t + 2 S = 15 S S = 1 2 f t 1 2 f t 1 t = 12 S … i i From Eqs. (i) and (ii), we have 12 S S = f t 1 t