A train starts from rest and travels in a straight line with acceleration 1.5 m/

Question

A train starts from rest and travels in a straight line with acceleration 1.5 m/s2 for 30 seconds. It then travels with a constant speed for 2 minutes. It then starts do decelerate at a constant rate of 3 m/s2 until it comes to a complete stop. Calculate:
a) (4 pts) The speed of the train at the end of the first portion of the trip (acceleration)?
b) (4 pts) The distance covered in the first portion of the trip?
c) (4 pts) The distance covered in the second portion of the trip (constant speed)?
d) (4 pts) Total distance traveled?
e) (4 pts) Average velocity over the duration of the trip?

Explanation / Answer

a) vf = vi + at vf = (1.5 m/s/s)(30 s) vf = 45 m/s b) d = vt + 0.5at^2 d = 0.5(1.5 m/s/s)(30 s)^2 d = 675 m c) d = vt d = (45 m/s)(120 s) d = 5400 m d) vf = vi + at 0 = 45 m/s + (-3 m/s/s)t t = 15 s d = vt + 0.5at^2 d = (45 m/s)(15 s) + 0.5(-3 m/s/s)(15 s)^2 d = 337.5 m 675 m + 5400 m + 337.5 m = 6412.5 m e) 30 s + 120 s + 15 s = 165 s (6412.5 m) / (165 s) = 38.86 m/s

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