The relation between velocity v and displacem | vedclass

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(C) Given the relation between velocity and displacement is $v = x^2$.We know that acceleration $a$ can be expressed as $a = v \frac{dv}{dx}$.First,di

Vedclass · Accepted Answer

$54$

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(C) Given the relation between velocity and displacement is $v = x^2$.We know that acceleration $a$ can be expressed as $a = v \frac{dv}{dx}$.First,differentiate $v$ with respect to $x$: $\frac{dv}{dx} = \frac{d}{dx}(x^2) = 2x$.Now,substitute $v$ and $\frac{dv}{dx}$ into the acceleration formula:$a = (x^2) \cdot (2x) = 2x^3$.To find the acceleration at $x = 3 \ m$,substitute the value of $x$ into the expression:$a = 2(3)^3 = 2 \cdot 27 = 54 \ m/s^2$.

The relation between velocity $v$ and displacement $x$ is $v = x^2$. Find the acceleration at $x = 3 \ m$.

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