EXAMPLE $8($Practical stopping distance and perception$/$reaction time$)$

A car is traveling up a $2\%$ grade at $70m\frac{i}{h}$ on good, wet pavement. The driver brakes to

try to avoid hitting stopped traffic that is $250$ ft ahead. The driver's reaction time is $0\mathrm{.}5$ s $.$

At first, when the driver applies the brakes, a software flaw causes the

antilock braking system to fail $($brakes work in non$-$antilock mode with $80\%$ efficiency$),$

leaving $80$ ft skid marks. After the $80$ ft skid, the antilock brakes work with $100\%$

efficiency. How fast will the driver be going when the stopped traffic is hit if the

coefficient of rolling resistance is constant at $0\mathrm{.}013?($Assume minimum theoretical

stopping distance and ignore aerodynamic resistance.$)$

SOLUTION:

EXAMPLE $6($Braking efficiency and Practical stopping distance$)$

A car $W=2200lb,C{D}_D=0\mathrm{.}25,A_f=21\mathrm{.}5f{t}^2$ has an antilock braking system that gives it a

braking efficiency of $100\%.$ The car's stopping distance is tested on a level roadway with

poor, wet pavement $($with tires at the point of impending skid$),$ and $=0\mathrm{.}00238$

slugs$/f{t}^3.$ How inaccurate will the stopping distance predicted by the practical stopping$-$

distance equation be compared with the theoretical stopping distance, assuming the car

is initially traveling at $60m\frac{i}{h}?$ How inaccurate will the practical stopping$-$distance

equation be if the same car has a braking efficiency of $85\%?$

SOLUTION: