The distance travelled by an object in time t | vedclass

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(D) The distance $s$ is given as a function of time $t$ by the equation $s = 2.5 t^2$.The instantaneous speed $v$ is defined as the time derivative of

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$25$

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(D) The distance $s$ is given as a function of time $t$ by the equation $s = 2.5 t^2$.The instantaneous speed $v$ is defined as the time derivative of the distance $s$,given by $v = \frac{ds}{dt}$.Substituting the expression for $s$: $v = \frac{d}{dt}(2.5 t^2)$.Using the power rule for differentiation,$\frac{d}{dt}(t^n) = n t^{n-1}$,we get $v = 2.5 	imes 2 	imes t = 5t$.To find the instantaneous speed at $t = 5\,s$,substitute $t = 5$ into the expression for $v$:$v = 5 	imes 5 = 25\,m/s$.

The distance travelled by an object in time $t$ is given by $s = 2.5 t^2$. The instantaneous speed of the object at $t = 5\,s$ will be $....\,m/s$.

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