Question

A block is resting over a rough horizontal floor. At $t=0$, a time varying force starts acting on it, the force is described by equation $F=kt$, where $k$ is constant and $t$ is in seconds. Mark the correct statement(s) for this situation.

• A. Curve $1$ shows acceleration-time graph
• B. Curve $2$ shows acceleration-times graph
• C. Curve $3$ shows velocity-time graph
• D. Curve $4$ shows displacement-time graph

Answer 1

Answer: (B), (C), (D)

Curve $3$ shows velocity-time graph
Curve $4$ shows displacement-time graph
Curve $2$ shows acceleration-times graph

For some time, the block won't move due to friction force. When $F>f_L$, the motion of block starts.

$a=\frac{F-f_k}{m}=\frac{kt-f_k}{m}$
$\Rightarrow$ $\frac{dv}{dt}=a=\frac{kt-f_k}{m}$ $\Rightarrow$ $v=\frac{\frac{k{t}^2}{2}-f_{k}t}{m}$

$\Rightarrow \frac{ds}{dt}=v=\frac{\frac{k{t}^2}{2}-f_{k}t}{m}\Rightarrow s=\frac{\frac{k{t}^3}{2}-\frac{f_k{t}^2}{2}}{m}$