Answer:
0.79 s
Explanation:
We have to calculate the employee acceleration, in order to know the minimum time. According to Newton's second law:
[tex]\sum F_x:f_{max}=ma_x\\\sum F_y:N-mg=0[/tex]
The frictional force is maximum since the employee has to apply a maximum force to spend the minimum time. In y axis the employee's acceleration is zero, so the net force is zero. Recall that [tex]f_{max}=\mu N[/tex]
Now, we find the acceleration:
[tex]\mu N=ma_x\\\mu mg=ma_x\\a_x=\mu g\\a_x=0.83(9.8\frac{m}{s^2})\\a_x=8.134\frac{m}{s^2}[/tex]
Finally, using an uniformly accelerated motion formula, we can calculate the minimum time. The employee starts at rest, thus his initial speed is zero:
[tex]x=v_0t+\frac{1}{2}a_xt^2\\2x=a_xt^2\\t=\sqrt{\frac{2x}{a}}\\t=\sqrt{\frac{2(3.2m)}{8.134\frac{m}{s^2}}}\\t=0.79 s[/tex]
