Question

A cube of mass 10kg is at rest on a horizontal surface when it is subjected to a horizontal for P that varies with time t as P=20t. If the static and kinetic coefficients of friction are both 0.4, calculate the velocity of the cube after 5s.

Answer 1

The Newton's second law says

$$m\frac{dv}{dt}=F=20t-\mu mg$$

$$v(t)=v(0)+10t^2/m-\mu gt$$

$$v(5)=0+10*5^2/10-0.4*9.8*5=5.4\:\rm m/s$$