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Question

The equation of motion of a particle started at $t = 0$ is given by $x = 5 sin (20 t + \frac{π}{3})$ , where $x$ is in cm and $t$ in sec. When does the particle first have maximum speed?

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Updated on : 2022-09-05

Solution

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$X = 5 sin (20 t + \frac{π}{3})$
$v = \frac{d x}{d t} = 100 cos (20 t + \frac{π}{3})$
$a = \frac{d v}{d t} = - 2000 sin (20 t + \frac{π}{3})$
v=0 for the first time when,
$20 t + \frac{π}{3} = \frac{π}{2}$
$∴$ $t = \frac{π}{1 2 0}$ s

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