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# A wrench dropped from a state of rest at time t = 0 travels a distance$s(t) = 4.9t^2 m$in t seconds. Estimate the instantaneous velocity at t = 3.

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A wrench dropped from a state of rest at time $t = 0$ travels a distance $s(t) = 4.9t^2$ m in t seconds. We need to find instantaneous velocity at $t = 3$. Make a table of five average velocity for short interval .average velocity can be find out using the formula $\fbox{Average Velocity $=\dfrac{\Delta s}{\Delta t}$}$

Consider first interval$[t_o, t_1] =[3,3.1]$

\begin{align*} \Delta t &=3.1-3.0=0.1\\ \Delta s&=s(3.1)-s(3.0)\\ &=4.9 \times 3.1^2-4.9 \times 3.0^2\\ &=47.089-44.1\\ \Delta s&=2.989\\ Average\ Velocity &=\dfrac{\Delta s}{\Delta t}\\ &=\dfrac{2.989}{0.1}\\ Average\ Velocity &=29.89 \ \ \text{m/s} \end{align*}

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