A car starting from rest accelerates at the rate f through a distance s, then continues at constant

Question

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

Accepted Answer

Let the car takes time t1 to reach from O to A a distance s with acceleration f and t2 to come to rest from B to C with deceleration velocity at A = velocity at Bf t1 = t2or t2 = 2t1Now, s1 = 0 + ft12 = ft12 = s (given)s2 = (f t1)t (&#8757; v = 0 + f t1)s3 = (f t1) t2 - = f t1 . 2t1 - (2t1)2= 2f t12 - f t12 = f t12But, s1 + s2 + s3 = 15 s&#8756; f t12 + f t1t + f t12 = 15sf t12 + f t1t = 15sft1t = 12 s = 12f t12or t1 = &#8756; s = Thus, none of the option is correct.

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