In the Daytona 500 auto race, a Ford Thunderbird and a Mercedes Benz are moving side by side down a straightaway at 73.5 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 73.5 m/s after a distance of 400 m. At this point how far has the Thunderbird fallen behind the Mercedes Benz, which has continued at a constant speed

Thunderbird has fallen behind the Mercedes Benz by 1017.49 m

Explanation:

Given the data in question;

initial speed of the ford u1 = 73.5 m/s

distance d1 = 250 m

t1 = 5.00 s

d2 = 400 m

Now, let the time taken to stop be t2 and deceleration is a1

so,

a1 = u1² / (2 × d1)

a1 = (73.5)² / (2 × 250)

a1 = 10.8045 m/s²

Now , for acceleration is a2

a2 = v² / (2 × d2)

a2 = (73.5)² / (2 × 400)

a2 = 6.7528 m/s²

total time spend = 5 + u/a1 + u/a2

total time spend = 5 + (73.5/10.8045) + (73.5/6.7528)

total time spend = 22.687 sec

Now, distance Mercedes is ahead = 22.687 × 73.5 - 400 - 250

= 1667.4945 - 400 - 250

= 1017.49 m

Therefore, Thunderbird has fallen behind the Mercedes Benz by 1017.49 m

can be answered using momentum.

momentum = p

p1= mass1 * velocity1

p1 = p2

therefore

p1 = 6kg * 4m/s

p1 = 24kgm/s

p2=m2 * v2

24 kgm/s = 7kg * v2

v2 = 24 kgm/s / 7kg

v2= 3.42 m/s