Question

A block of mass 1 kg is moving at $t=0$ with speed 2 m/s on rough horizontal surface with coefficient of friction 0.2. A horizontal force F is applied in the same direction of velocity which varies with time as shown in figure(b). Find the speed of block at $t=3s$ $(g=10m/s^2)$

• A. 1 m/s
• B. zero
• C. 5 m/s
• D. 2 m/s

Answer 1

The correct option is B zero

From the given figure we get

$\begin{array}{c}f=\{\begin{array}{c}2tt<1\\ 2\left(t-1\right)1<t<2\\ 2\left(t-2\right)2<t<3\end{array}\\ Now,\\ Netforceonblock\\ ma=F-\mu gm\\ a=\frac{F}{m}-\mu g\\ a=\{\begin{array}{c}2tt<1\\ 2\left(t-1\right)1<t<2\\ 2\left(t-2\right)2<t<3\end{array}\\ Then\\ {\int }_2^v\frac{dv}{dt}={\int }_0^{1}2\left(t-1\right)dt+{\int }_1^{2}2\left(t-2\right)dt+{\int }_2^{3}2\left(t-3\right)dt\\ v-2={\int }_0^1{t}^2-2t+{\int }_1^2\left(t^2-4t\right)+{\int }_2^3{t}^2-6t\\ v-2=\left(1-2\right)+\left(4-80+\left(1-4\right)\right)\\ v-2=\left(-1\right)+\left(-1\right)+\left(-1\right)\\ \therefore v=-1m/s\end{array}$

Now,

Triction is sec adjusting force it will not increase the velocity in the direction

Hence, velocity turns zero after 2s.

So, option $B$ is the correct answer.