Question

A wrench dropped from a state of rest at time t = 0 travels a distance

s(t)=4.9t2ms(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=0t = 0 travels a distance s(t)=4.9t2s(t) = 4.9t^2 m in t seconds. We need to find instantaneous velocity at t=3t = 3. Make a table of five average velocity for short interval .average velocity can be find out using the formula $\fbox{Average Velocity =ΔsΔt=\dfrac{\Delta s}{\Delta t}}$

Consider first interval[to,t1]=[3,3.1][t_o, t_1] =[3,3.1]

Δt=3.13.0=0.1Δs=s(3.1)s(3.0)=4.9×3.124.9×3.02=47.08944.1Δs=2.989Average Velocity=ΔsΔt=2.9890.1Average Velocity=29.89  m/s\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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