Question

An army vehicle of mass 1000 kg is moving with a velocity of 10m/s and is acted upon by a forward force of 1000N due to engine and a retarding force of 500N due to friction. What will be its velocity after 10 seconds?

Answer 1

$$\begin{gathered} \mathrm{Given}, \\ \mathrm{Mass}\mathrm{of}\mathrm{the}\mathrm{army}\mathrm{vehicle},m=1000\mathrm{kg} \\ \mathrm{velocity}\mathrm{of}\mathrm{army}\mathrm{vehicle},u=10\mathrm{m}{\mathrm{s}}^{-1} \\ \mathrm{Forward}\mathrm{force},F=1000\mathrm{N} \\ \mathrm{Frictional}\mathrm{force},f=500\mathrm{N} \\ \mathrm{Time},\mathit{}t=10\mathrm{s} \\ \mathrm{Net}\mathrm{force},F\text{'}=1000-500=500\mathrm{N} \\ \mathrm{Let}v\mathrm{be}\mathrm{the}\mathrm{velocity}\mathrm{after}10\mathrm{s}. \\ \mathrm{From}\mathrm{the}\mathrm{relation} \\ F\text{'}=\frac{m\left(v-u\right)}{t} \\ \Rightarrow 500=\frac{1000\left(v-10\right)}{10} \\ \Rightarrow 500=100v-1000 \\ \Rightarrow 100v=1500 \\ \Rightarrow v=\frac{1500}{100}=15\mathrm{m}{\mathrm{s}}^{-1} \end{gathered}$$