Question

the engineer of a passenger train traveling at 100 ft/sec sights a freight train whose caboose is 600 ft ahead of the same track. The freight train is traveling in the same direction as the passenger train with a velocity of 30 ft/sec. The engineer of the passenger train immediately applies the brake, causing a constant acceleration of 4 ft/sec^2, while the freight train continues with constant speed, a) will there be a collision? b) if so, where will it take place?

Answer 1

how long does it take to get from 100 to 30?

v = vi + a t
30 = 100 - 4 t
4 t = 70
t = 17.5 s
how far did we go?
average speed = 130/2 = 65
65*17.5 = 1137.5 ft

how far did the freight go?
30 * 17.5 = 525

525 + 600 = 1125 ft
CRASH

for part b
x1 = 100 t - 2 t^2
x2 = 600 + 30 t
when does x1 = x2?
600 + 30 t = 100 t - 2 t^2
solve quadratic for t
then get x = x1 = x2