A car starts from rest and accelarates at uniform rate of 5meter/ second squarefor some time then moves with constant speed for some time and then retards at the same uniform rate and come to rest. Total time taken for journey is 25s and average speed for the journey is 20m/s How long does the car move with constant speed.

Asked by yasho1710 | 4th Sep, 2010, 08:53: AM

Expert Answer:

Make a v-t graph. The area under the v-t graph gives us the distance, which is also equal to average speed *total time = 25 *20 = 500m
v-t graph will have three parts, one for the acceleration, second for the constant speed and third for deceleration. Since, the acceleration gives us the slope of v-t graph, so the slope of acceleration curve and deceleration curve is +5 and -5 respectively. Now, if you will assume that the time for which the body remains in acceleration as x sec, then the time taken for deceleration is also x sec. (By symmetry of the curve). Hence, the time for which the body moves with a constant speed is (25-2x) sec. Now, you can calculate area under the graph in terms of x, with the slope known as 5 and base as x, (25-2x) and x respectively. You will get a quadratic equation and on solving it you will get x = 5 sec, which gives the time for which the body moves with constant speed as 15 sec. 

Answered by  | 6th Sep, 2010, 11:36: PM

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