KCET · Physics · Work Power Energy
A truck accelerates from speed \(v\) to \(2 v\). Work done in during this is
- A three times as the work done in accelerating it from rest to \(v\)
- B same as the work done in accelerating it from rest to \(\mathrm{V}\)
- C four times as the work done in accelerating it from rest to \(v\)
- D less than the work done in accelerating it from rest to \(v\)
Answer & Solution
Correct Answer
(A) three times as the work done in accelerating it from rest to \(v\)
Step-by-step Solution
Detailed explanation
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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