speed equation?? Car A and Car B

Question

Car A is traveling at 75mph and passess Car B sitting on the side of the road stopped. There is a 30 second delay before Car B starts and accelerates to catch up to Car A. Car B catches up to Car A approx 2.5 miles down the road. At what speed did Car B have to accelerate to in order to catch up to Car A??

Answer 1

A goes 75 mph

B is at a stop as A goes by

30 seconds later B starts and accelerates and catches up to A 2.5 miles down the road

at what speed did B have to accelerate to catch up to A??

d = rt, for A

2.5 = 75t

t = 2.5/75 = .1/3 = 1/30 hr = 2 minutes = 120 seconds

for B convert 120-30 = 90 seconds to 1.5 minutes = 1.5/60 hours = 15/600 = 1/36 hr.

d =rt

2.5 = r/36

r = 36(2.5) = 100 mph average

convert 100 to accelerating from 0 to ?

s(t) = at^2

s'(t) = 2at = 100

a = 50/t = 50/1/36 = 50x36 = 1800 miles per hour per hour

or

integrate velocity

v(t) = s'(t) = 2at

integral of 2at evaluated from t=0 to t=1/36

= at^2 0 to 1/36 = 100

a(1/36)^2 = 100

a = 100(36^2) = 129,600 mph/h

one of the two, 1,800 mph/h or 129,600 mph/h = a