Answer:
Time = 77.63 s
Distance = 3673.3 ft
Step-by-step explanation:
Using equation of motion
v = u + at'
50 = 6 * t'
t' = 50 / 6
t' = 8.33 s
v² = u² + 2a(s - s•)
50² = 0² + 2 * 6 * (s - 0)
2500 = 12 * s
s' = 2500 / 12
s' = 208.3 ft
At t' = 8.33 the distance traveled by the car is
s'' = v• * t'
s'' = 30 * 8.33
s'' = 250 ft
Now, the distance between the motorcycle and car is
6000 - 208.33 - 250 = 5541.67
For motorcycle, when passing occurs,
s = v• * t, x = 50 * t''
For the car, when passing occurs,
s = v• * t, 5541.67 - x = 30 * t''
Solving both simultaneously, we have
5541.67 - [50 * t''] = 30 * t''
5541.67 = 30t''+ 50t''
5541.67 = 80t''
t''= 5541.67 / 80
t''= 69.3 s, substituting t'' = 69.3 back, we have
x = 50 * 69.3
x = 3465 ft
Therefore for motorcycle,
t = 69.3 + 8.33
t = 77.63 s
S = 3465 + 208.3
s = 3673.3 ft