Answer
a) $s=10m$
b) $t=3.64s$
Work Step by Step
a) When the snowmobile is moving, it is under the influence of 2 opposing forces: drive force $D$ and kinetic friction $f_k$. The snowmobile goes at a constant speed, so we know these 2 forces are equal: $D=f_k=205N$
When the drive force is shut off, $f_k$ acts as the only force influencing the skier's motion by stopping it. $f_k$ opposes the motion in the opposite direction of the displacement, so $$W=(f_k\cos180)s=-f_ks (1)$$
According to the work-energy theorem, $W=\frac{1}{2}mv_f^2-\frac{1}{2}mv_0^2$
Because $v_f=0$, we can rewrite $W=-\frac{1}{2}mv_0^2 (2)$
From (1) and (2), we have $$-f_ks=-\frac{1}{2}mv_0^2$$ $$s=\frac{mv_0^2}{2f_k}$$
We have $m=136kg$, $v_0=5.5m/s$ and $f_k=205N$
$$s=10m$$
b) We can use the equations of kinematics to find $t$.
As $s=10m$, $v_0=5.5m/s$, $v_f=0$, we have $$s=\Big(\frac{v_f+v_0}{2}\Big)t$$ $$t=\frac{2s}{v_f+v_0}=3.64s$$
