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5.Work, Energy, Power and Collision
medium
The kinetic energy $K$ of a particle moving in a straight line depends upon the distance $s$ as $K = as^2$. The force acting on the particle is
A$2\,as$
B$2\,mas$
C$2\,a$
D$\sqrt {as^2}$
Solution
$\mathrm{k}=\mathrm{as}^{2} \Rightarrow \frac{1}{2} \mathrm{mv}^{2}=\mathrm{as}^{2}$
$\mathrm{v}^{2}=\frac{2 \mathrm{a}}{\mathrm{m}} \mathrm{s}^{2}$
differentiate $w.r. t.$ time
$2 \mathrm{v} \frac{\mathrm{dv}}{\mathrm{dt}}=\frac{2 \mathrm{a}}{\mathrm{m}} \times 2 \mathrm{s} \frac{\mathrm{ds}}{\mathrm{dt}}$
$\mathrm{F}=\mathrm{m} \frac{\mathrm{dv}}{\mathrm{dt}}=2 \mathrm{as}$
$\mathrm{v}^{2}=\frac{2 \mathrm{a}}{\mathrm{m}} \mathrm{s}^{2}$
differentiate $w.r. t.$ time
$2 \mathrm{v} \frac{\mathrm{dv}}{\mathrm{dt}}=\frac{2 \mathrm{a}}{\mathrm{m}} \times 2 \mathrm{s} \frac{\mathrm{ds}}{\mathrm{dt}}$
$\mathrm{F}=\mathrm{m} \frac{\mathrm{dv}}{\mathrm{dt}}=2 \mathrm{as}$
Standard 11
Physics
