Question 237: Work, Energy and Power & Circular Motion

Question

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 ____________.

Accepted Answer

The kinetic energy of a moving object of mass $$m$$ and velocity $$v$$ is given by the formula:
$$K = \frac{1}{2}mv^2$$
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:
$$E = \frac{1}{2}mu^2$$
The energy required to accelerate the car from $$u \mathrm{~m}/\mathrm{s}$$ to $$2u \mathrm{~m}/\mathrm{s}$$ is:
$$\begin{aligned} nE &= \frac{1}{2}m(2u)^2 - \frac{1}{2}mu^2 \\ &= 2mu^2 - \frac{1}{2}mu^2 \\ &= \frac{3}{2}mu^2 \\
&= 3E \end{aligned}
$$
$$ 	herefore $$ n = 3

Work, Energy and Power & Circular Motion

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 ____________.

Integer / Numeric Answer Type