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Q.
Energy required to accelerate a car from $10 \,m / s$ to $20\, m / s$ compared with that required to accelerate it frem $0$ to $10 \,m / s$ is
AMUAMU 2007
Solution:
$ K E_{1} =\frac{1}{2} m\left(v_{2}^{2}-v_{1}^{2}\right)$
$ \therefore K E_{1} =\frac{1}{2} m\left[(20)^{2}-(10)^{2}\right] $
$ \Rightarrow K E_{1} =\frac{1}{2} m(400-100) $
$ \Rightarrow K E_{1} =\frac{1}{2} m \times 300=150\, m$ ... (i)
$ K E_{2} =\frac{1}{2} m\left[(10)^{2}-0\right] $
$\Rightarrow KE _{2}=\frac{1}{2} m \times 100=50 \,m$ ... (ii)
From Eqs. (i) and (ii), we have
$KE _{1}=3 KE _{2}$