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A truck accelerates from speed $v$ to $2 v$. Work done in during this is
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The correct answer is:
three times as the work done in accelerating it from rest to $v$
Work done to accelerate from 0 to $v$ is, $W_{1}=\frac{1}{2} m v^{2}$ Work done to accelerate from $v$ to $2 v$ is,
$\begin{aligned}
W_{2} &=\frac{1}{2} m(2 v)^{2} \\
\Delta W &=W_{2}-W_{1}=\frac{1}{2} m(2 v)^{2}-\frac{1}{2} m v^{2} \\
\Rightarrow \quad & 4 W_{1}-W_{1}=3 W_{1}
\end{aligned}$
$\begin{aligned}
W_{2} &=\frac{1}{2} m(2 v)^{2} \\
\Delta W &=W_{2}-W_{1}=\frac{1}{2} m(2 v)^{2}-\frac{1}{2} m v^{2} \\
\Rightarrow \quad & 4 W_{1}-W_{1}=3 W_{1}
\end{aligned}$
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