particle starts moving rectilinearly at time t=0 such that its velocity v changes with time t according to equation v=t2−t where t is in seconds and v in ms−1. Find the time interval for which the particle retards.0.5s < t < 1 s0.5s < t < 2 s0.5s < t < 3 s0.5s < t < 5 s
Question
particle starts moving rectilinearly at time t=0 such that its velocity v changes with time t according to equation v=t2−t where t is in seconds and v in ms−1. Find the time interval for which the particle retards.0.5s < t < 1 s0.5s < t < 2 s0.5s < t < 3 s0.5s < t < 5 s
Solution
The particle retards when its velocity decreases, i.e., when dv/dt < 0.
Given v = t^2 - t, we can differentiate this with respect to time to get dv/dt = 2t - 1.
Setting this less than zero gives us the condition for retardation:
2t - 1 < 0 => 2t < 1 => t < 0.5 s
However, this is not in any of the given options. The particle does not retard in any of the given time intervals.
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