Answer:
FT is 1020.6 meters (1640.6 meters - 620 meters) far from MB
Explanation:
First you have to consider that the Ford Thunderbird (FT) follows a rectilinear motion with varying acceleration, while Mercedez Benz (MB) has a constant velocity (no acceleration). So if you finde the time spent by FT in each section, and the distance, then you will find the distance for MB.
1) Vf² = Vi² + 2ad, where Vf: final velocity, Vi: ionitial velocity, a: acceleration and d: distance.
For the first portion (0 m/s)² = (78.5 m/s)² + 2a(250 m) ⇒
-(78.5 m/s)² / 2(250m) = a ⇒ a = -12.3 m/s².
Now, you can find the corresponding time for this section with the following formule: Vf = Vi + at ⇒ 0 m/s = 78.5 m/s + (-12.3 m/s²) t
⇒ t= (-78.5 m/s)/ (-12.3 m/s²) ⇒ t= 6.4 seconds.
2) Then FT spent 5 seconds in the pit.
3) The the FT accelerates until reach 78.5 m/s again in a distance of 370 m.
Vf² = Vi² + 2ad ⇒ (78.5 m/s)² = (0 m/s)² + 2a(370 m)
⇒ (78.5 m/s)²/ 2(370 m) = a ⇒ a = 8.3 m/s²
Then, Vf = Vi + at ⇒ 78.5 m/s = 0 m/2 + (8.3 m/s²) t
⇒ (78.5 m/s)/(8.3 m/s²) = t ⇒ t = 9.5 seconds.
4) Summarizing, the FT moves 620 meters (250 + 370 mts) in 20.9 seconds ( 6.4 s + 5 s + 9.5 s).
5) During this time, MB moves
Velocity = distance/ time ⇒ Velocity x time = Distance
⇒ Distance = (78.5 m/s) x (20.9 seconds) ⇒ Distance = 1640.6 meters
6) Finally, the FT is 1020.6 meters (1640.6 meters - 620 meters) far from MB
