In the Daytona 500 auto race, a Ford Thunderbird and a Mercedes Benz are moving side by side down a straightaway at 71.0 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 71.0 m/s after a distance of 300 m. At this point how far has the Thunderbird fallen behind the Mercedes Benz, which has continued at a constant speed?

Answer 1

time to slow down:
Vi = 71.0 m/s
average speed during slowing = 71/2 = 35.5 m/s
250 = 35.5 t
t = 7.04 seconds to stop
T now at 250 meters
M now at 7.04*71 = 500 meters (twice as fast of course)
after 5 second stop
T still at 250 meters
M now at 500 + 5*71 = 855 meters
now T 300 meters at 35.5 m/s again so 300/35.5 = 8.45 s
T now at 250 + 300 = 550 meters
M now at 855 + 8.45*71 = 1455 meters
1455 - 550 = ?

Answer 2

v^2 = 2as
71^2 = 500a
a = -10 m/s^2
t1 = 71/10 = 7.1s to stop

Now work the same magic with s=300 to find the time t3 to accelerate, then add the three times together

The Benz has gone x = 71.0 (t1+5+t3) meters
so the T-bird is x-(250+300) meters behind

Answer 3

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