$13\mathrm{.}137$ A crash test is performed between an SUV A and a $2500-lb$ compact car $B.$ The compact car is stationary before the impact and has its brakes applied. A transducer measures the force during the impact, and the force $P$ varies as shown. Knowing that the coefficients of friction between the tires and road are ${}_s=0\mathrm{.}9$ and ${}_k=0\mathrm{.}7,$ determine $($a$)$ the time at which the compact car will start moving, $($b$)$ the maximum speed of the car, $($c$)$ the time at which the car will come to a stop.

Fig. P$13\mathrm{.}137$