A subway train starts from rest at a station and accelerates at a rate of 1.60 m/s2 for 14.0s. It runs at a constant speed for 70.0 s and then slows down at a rate of -3.50 m/s2 until it stops at the next station.

Question

A subway train starts from rest at a station and accelerates at a rate of 1.60 m/s2 for 14.0s. It runs at a constant speed for 70.0 s and then slows down at a rate of -3.50 m/s2 until it stops at the next station.
a) Sketch a position vs. time graph for this problem.
b) Sketch a velocity vs. time graph for this problem.
c) Find the total distance covered by the train.

Henry · Answer

c. d1 = 0.5a*t^2 = o.8*14^2 = 156.8 m.
V = a*t = 1.6 * 14 = 22.4 m/s.
d2 = 22.4m/s * 70s = 1568 m.

V^2 = Vo^2 + 2ad.
d3 = (V^2-Vo^2)/2a.
d3 = (0-(22.4)^2)/-7 = 71.7 m.

Dt=d1+d2+d3 = 156.8+1568+71.7 = 1797 m.