A car with $17-$inch radius wheels is traveling at maximum power on a road with a $-3\%$ grade

with a gear reduction ratio of $3\mathrm{.}5$ and driveline slippage of $1\mathrm{.}5\%.$ The car has a braking efficiency

of $99\%$ when antilock brakes $($ABS$)$ work, and a torque$/$engine speed curve of the form:

$M_e=7n_e-0\mathrm{.}08n_e^2$

with $M_e$ in $ft-lb$ and ne in revolutions per second.

While traveling on poor, wet road, the driver spotted a stalled truck up ahead. He was able to come

to a complete stop just before hitting the truck. The final $200$ feet was on packed ice and the car's

ABS did not work which reduced its braking efficiency to $80\%.$ Assume $f_{rl}=0\mathrm{.}02$ when the brakes

are locked. You will need to compute $f_{rl}$ when the brakes are not locked. What is the minimum

theoretical stopping distance from the stalled truck to where the driver first spotted the truck? For

theoretical stopping distance, ignore air resistance. What is the car's deceleration rate in the last

$200$ feet?