A car accelerates from rest to $u \mathrm{~m} / \mathrm{s}$. The energy spent in this process is E J. The energy required to accelerate the car from $u \mathrm{~m} / \mathrm{s}$ to $2 \mathrm{u} \mathrm{m} / \mathrm{s}$ is $\mathrm{nE~J}$. The value of $\mathrm{n}$ is ____________.
Answer (integer)
3
Solution
The kinetic energy of a moving object of mass $m$ and velocity $v$ is given by the formula:
<br/><br/>
$K = \frac{1}{2}mv^2$
<br/><br/>
The work done in accelerating an object from rest to velocity $v$ is equal to its change in kinetic energy. Therefore, the energy spent in accelerating the car from rest to $u \mathrm{~m}/\mathrm{s}$ is:
<br/><br/>
$E = \frac{1}{2}mu^2$
<br/><br/>
The energy required to accelerate the car from $u \mathrm{~m}/\mathrm{s}$ to $2u \mathrm{~m}/\mathrm{s}$ is:
<br/><br/>
$$\begin{aligned} nE &= \frac{1}{2}m(2u)^2 - \frac{1}{2}mu^2 \\\\ &= 2mu^2 - \frac{1}{2}mu^2 \\\\ &= \frac{3}{2}mu^2 \\\\
&= 3E \end{aligned}
$$
<br/><br/>$\therefore$ n = 3
About this question
Subject: Physics · Chapter: Work, Energy and Power · Topic: Work Done by a Force
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