Question

A $20$ kg block is originally at rest on a horizontal surface for which the coefficient of friction is $0.6$. If a horizontal force F is applied such that it varies with time as shown in figure. Determine speed of block at $10$ sec.

Answer 1

The block starts from rest at time t = 0.

Let the speed of block at t = 10 seconds be v.

Area under the F-t graph = ${\int }_0^{t}Fdt$

= ${\int }_0^{t}Madt$

= ${\int }_0^{t}M\frac{dv}{dt}dt$

=M ${\int }_0^{v}dv$

= Mv

Therefore, the area under the graph from t=0 to t=10 seconds gives the velocity 'v' at t=10 seconds.

Area under the graph = $\frac{5\ast 200}{2}+(200\ast 5)$

= $1500$

Therefore,$Mv=1500$

$20\ast v=1500$

$v=75\frac{m}{s}$

The speed of the particle at t = 10 seconds is $75\frac{m}{s}$