In the Daytona 500 auto race, a Ford Thunderbird and a Mercedes Benz are moving side by side down a straight-away at 66.5 m/s. The driver of the Thunderbird realizes that she must make a pit stop, and she smoothly slows to a stop over a distance of 250 m. She spends 5.00 s in the pit and then accelerates out, reaching her previous speed of 66.5 m/s after a distance of 310 m. At this point how far has the Thunderbird fallen behind the Mercedes Benz, which has continued at a constant speed?

2 answers

time to slow: distance/avg velocity= 250/(66.5/2) seconds
time to accelerate: distance/avg velocity= 310/(66.5/2)seconds.

timelost= time to slow+timeinpit+time accelerating

distance front car went: 66.5*timelost
distance pit car went: 250+310

the difference in those is how far they are apart.
560 m