Question

A horizontal force acting on a box of mass 1$kg$ has a magnitude of $F=1t^{2}N$ , where $t$ is in second. If the box starts from rest, determine its speed at$t=3s$ . The coefficient of static friction and kinetic friction between the box and horizontal surface are ${\mu }_s=0.4$ and ${\mu }_k=0.3$ respectively. $(g=10m/s^2)$

• A. 19 m/s
• B. 1.3 m/s
• C. 3.33 m/s
• D. 10.2 m/s

Answer 1

The correct option is C 3.33 m/s

$\begin{array}{c}F=t^2\\ fsmax=\frac{4}{10}\times 10=4N\\ \therefore att=2blockstartsmoveing\\ \left(t^2-3\right)=ma\\ \Rightarrow \frac{dv}{dt}=\left(t^2-3\right)\\ \Rightarrow {\int }_0^{v}dv={\int }_L^3\left(t^2-3\right)dt\\ \Rightarrow v=\frac{1}{3}\left[27-8\right]-3\left(1\right)\\ =3.33m/s\\ \therefore Option\left(c\right)iscorrect.\end{array}$