The displacement of an object attached to a s | vedclass

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(B) The displacement equation is given by $x = 2 	imes 10^{-2} \cos(\pi t)$.To find the velocity $v$, we differentiate the displacement with respect

Vedclass · Accepted Answer

$0.5$

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(B) The displacement equation is given by $x = 2 	imes 10^{-2} \cos(\pi t)$.To find the velocity $v$, we differentiate the displacement with respect to time $t$:$v = \frac{dx}{dt} = \frac{d}{dt} [2 	imes 10^{-2} \cos(\pi t)] = -2 	imes 10^{-2} \pi \sin(\pi t)$.The speed is the magnitude of velocity, $|v| = |2 	imes 10^{-2} \pi \sin(\pi t)|$.For the speed to be maximum, the value of $|\sin(\pi t)|$ must be $1$.This occurs when $\sin(\pi t) = 1$ or $\sin(\pi t) = -1$.The first time this occurs is when $\sin(\pi t) = 1$, which corresponds to $\pi t = \frac{\pi}{2}$.Solving for $t$, we get $t = \frac{1}{2} = 0.5 	ext{ s}$.

The displacement of an object attached to a spring and executing simple harmonic motion is given by $x = 2 \times 10^{-2} \cos(\pi t) \text{ m}$. The time at which the maximum speed first occurs is (in $\text{ s}$)

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