the maximum speed of a bus is 72 km/hr , it accelerated uniformly at a rate 1m/s^2 and retardes at a rate of 4m/s^2, find the least time in which it can do a journey of 1km and also draw the v-t curve.

Suppose the car’s acceleration is a_{1} = 1 m/s^{2} for time t_{1} during which its maximum velocity ‘v’ is 72 km/h or 20 m/s.

Now, the time taken by the car to cover the said distance will be minimum if the average velocity of the car is maximum. This is possible only when the decelerating time or slowing down time is minimum. This can be found by differentiating *S _{2}* w.r.t.

*t*and equating it to zero.

_{2}So, the least time to cover 1 km is = *t*_{1}* + t*_{2}* *= 48.59 s

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