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Find the average velocity of a particle ...

Find the average velocity of a particle moving along a straight line such that its velocity changes with time as `v (m//s) = 4 sin. (pi)/(2) t`, over the time interval `t = 0` to `t = (2n - 1) 2` seconds. (n being any `+` ve integer).

Text Solution

Verified by Experts

Displacement over the interval `t = 0` to `t = 2 (2n - 1) s`
`s = 4 underset(0)overset(2(2n - 1))int sin ((pi)/(2) t) dt`
`= - (8)/(pi) [cos ((pi)/(2)t)]_(0)^(2(2n - 1)) = (16)/(pi) m`
`:.` Average velocity `= (16)/(2(2n - 1)pi) = (8)/((2n - 1)pi) m//s`
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Knowledge Check

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