A car accelerates from rest of u m s - 1 . The energy spent in this process is E J . The energy required to accelerate the car from u m s - 1 to 2 u m s - 1 is n E J . The value of n is _____.

Question

TestHub · Accepted Answer

The kinetic energy of a moving particle is given by
$E = \frac{1}{2} m u^{2} . . . (1)$
When the final velocity of the particle becomes twice the initial velocity, the kinetic energy of the particle can be written as
$\begin{array}{rcl} n E & = & \frac{1}{2} m \{(2 u)^{2} - u^{2}\} \\ = & \frac{1}{2} m (3 u^{2}) . . . (2) \end{array}$
Divide equation (2) by equation (1) and solve to calculate the value of $n$ .
$\begin{array}{rcl} \frac{n E}{E} & = & \frac{\frac{1}{2} m (3 u^{2})}{\frac{1}{2} m u^{2}} \\ \Rightarrow & n = 3 \end{array}$

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