(A) According to the work-energy theorem,the work done is equal to the change in kinetic energy.Work done to accelerate from $0$ to $v$ is $W_1 = \fra

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three times the work done in accelerating it from rest to $v$

(A) According to the work-energy theorem,the work done is equal to the change in kinetic energy.Work done to accelerate from $0$ to $v$ is $W_1 = \frac{1}{2}mv^2 - 0 = \frac{1}{2}mv^2$.Work done to accelerate from $v$ to $2v$ is $W_2 = \Delta K = \frac{1}{2}m(2v)^2 - \frac{1}{2}mv^2$.$W_2 = \frac{1}{2}m(4v^2) - \frac{1}{2}mv^2 = 2mv^2 - 0.5mv^2 = 1.5mv^2$.Comparing $W_2$ with $W_1$:$W_2 = 3 \times (\frac{1}{2}mv^2) = 3W_1$.Therefore,the work done is three times the work done in accelerating it from rest to $v$.

Class 11 Physics Work, Energy, Power and Collision Work Energy Theorem and Conservation of Mechanical Energy

Medium

$A$ truck accelerates from speed $v$ to $2v$. The work done during this process is:

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

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Work, Energy, Power and Collision

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Work Energy Theorem and Conservation of Mechanical Energy

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$A$ truck accelerates from speed $v$ to $2v$. The work done during this process is:

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