Question

A truck accelerates from speed $\upsilon \,to\, 2\upsilon$. Work done in during this is

• A. three times as the work done in accelerating it from rest to $\upsilon$
• B. same as the work done in accelerating it from rest to $\upsilon$
• C. four times as the work done in accelerating it from rest to $\upsilon$
• D. less than the work done in accelerating it from rest to $\upsilon$

Answer 1

Answer: (A)

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
$W_{2} =\frac{1}{2} \,m\,(2 v)^{2} $
$\Rightarrow \Delta W =W_{2}-W_{1}=\frac{1}{2} \,m(2 v)^{2}-\frac{1}{2} \,m v^{2} $
$=4\, W_{1}-W_{1}=3 \,W_{1}$