Physics - NLM Question with Solution | TestHub

Given, rate of decrease in kinetic energy $\frac{\mathrm{dk}}{\mathrm{dt}}=9.6\mathrm{J}/\mathrm{s}$ When, speed, $\mathrm{v}=3\mathrm{m}/\mathrm{s}$ then force $\mathrm{F}=$ ? Kinetic energy $\mathrm{k}=\frac{1}{2}{\mathrm{mv}}^2$ differentiating with respect to ' $t$ ', we have $\begin{array}{rl}& \frac{\mathrm{dk}}{\mathrm{dt}}=\frac{1}{2}\mathrm{m}\cdot 2\mathrm{v}\frac{\mathrm{dv}}{\mathrm{dt}}=\mathrm{v}\cdot \mathrm{m}\frac{\mathrm{dv}}{\mathrm{dt}}\\ & =v.m\frac{\mathrm{dp}}{\mathrm{dt}}\\ & \frac{\mathrm{dk}}{\mathrm{dt}}=\mathrm{v}.\mathrm{F}\left[\because \text{ force }\mathrm{F}=\frac{\mathrm{mdp}}{\mathrm{dt}}\right]\therefore \mathrm{F}=\frac{1}{\mathrm{v}}\cdot \frac{\mathrm{dk}}{\mathrm{dt}}\\ & =\frac{1}{3}\times 9.6=3.2\mathrm{N}\\ & \end{array}$