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Question

A car starts from rest. It has to cover a distance of 500 m and come to rest at the end of the journey. The coefficient of friction between the road and the tyre is 12. The minimum time in which the car can cover this distance is (g=10 m/s2)
  1. 10 seconds
  2. 30 seconds
  3. 15 seconds
  4. 20 seconds


Solution

The correct option is D 20 seconds
Maximum acceleration and maximum retardation of the car can be
μg or 12×10=5 m/s2
The corresponding velocity-time graph is as shown in the figure.
Let t0 be the time of acceleration and retardation. Then
vm=μgt0=5t0
Now, displacement = area under vt graph
500=12×2t0×5t0
or t0=10 seconds
Total time of journey is 2t0 or 20 seconds.
Hence, the correct answer is option (a).

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