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A body moves from rest with a constant acceleration. Which one of the following graphs represents the variation of its kinetic energy $K$ with the distance travelled $(x)$ ?
Options:
- A
- B
- C
- D
Solution:
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The correct answer is:
$\begin{aligned} & \text { } K=\frac{1}{2} m v^2, \text { where } v=0+a t \\ & \therefore \quad K=\frac{1}{2} m(a t)^2=\frac{1}{2} m a^2 t^2 \\ & \text { As } a=\left[L T^{-2}\right]=\text { constant } \\ & \therefore \quad L \propto T^2 \\ & \therefore \quad K=\frac{1}{2} m a^2 . L \text { or } K \propto L \text { or } x .\end{aligned}$
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