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Question

# A particle starts moving rectilinearly at time t = 0 such that its velocity ‘v’ changes with time ‘t’ according to the equation v=t2−t where t is in seconds and v in m/s. Find the time interval for which the particle retards.

A

t = 0 to t = 1 s

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B

t = 0.5 s to t = 1 s

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C

t = 0 to t = 0.5 s

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D

t > 1 s

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Solution

## The correct option is B t = 0.5 s to t = 1 s Velocity, v=t2−t Acceleration, a=dvdt=2t−1 The particle retards when acceleration is opposite to velocity. Now, v is positive when t > 1 s and negative when t < 1 s. Similarly, a is positive when t > 0.5 s and negative when t < 0.5 s. So, for the interval t = 0.5 s to t = 1 s, velocity and acceleration have opposite signs and the particle is retarding.

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