Work Energy Power

JEE Main level, numerical answer, medium

65 of 183

Question 65 of 183

A car accelerates from rest of ums−1um{s}^{-1}. The energy spent in this process is EJEJ. The energy required to accelerate the car from ums−1um{s}^{-1} to 2ums−12um{s}^{-1} is nEJnEJ. The value of nn is _____.

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Answer: 3

The kinetic energy of a moving particle is given by
E=12mu2...(1)E=\dfrac{1}{2}m{u}^{2}...(1)
When the final velocity of the particle becomes twice the initial velocity, the kinetic energy of the particle can be written as
nE=12m{(2u)2−u2}=12m(3u2)...(2)\begin{matrix}nE & = & \dfrac{1}{2}m\left\{(2u{)}^{2}-{u}^{2}\right\} \\ & = & \dfrac{1}{2}m\left(3{u}^{2}\right)...\left(2\right)\end{matrix}
Divide equation (2) by equation (1) and solve to calculate the value of nn.
nEE=12m(3u2)12mu2⇒n=3\begin{matrix}\dfrac{nE}{E} & = & \dfrac{\dfrac{1}{2}m\left(3{u}^{2}\right)}{\dfrac{1}{2}m{u}^{2}} \\ & \Rightarrow & n=3\end{matrix}

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