Question

A train travelling along a straight track starts from rest at point A and accelerates uniformly to 20m/s in 20s. It travels at this speed for 60s then slows down uniformly to rest in 40s at point C. it stays at rest at C for 30s, then reverses direction accelerating uniformly to 10m/s in 10s. It travels at this speed for 30s, then slows down uniformly to rest in 10s when it reaches point B.
a) Plot a graph of the motion of the train
b) Use your graph to calculate
i) The trains displacement from point A when it reaches point C
ii) The trains displacement from point A when it reaches point B
iii) The trains acceleration each time its speed changes

Answer 1

Let's find the train's displacement from point A when it reaches point C. We should calculate the area of the trapeze ADEC:

$S_1=\frac{60+120}{2}\cdot{}20=1800$ m.

Now let's find the train's displacement from point A when it reaches point B. We should calculate the difference of areas of the trapeze ADEC and trapeze FGHB:

$S_2=S_1-\frac{50+30}{2}\cdot{}10=1800-400=1400$ m.

Let's find the trains acceleration each time its speed changes.

$0\eqslantless{}t\eqslantless{}20,$ $a_1=\frac{20-0}{20}=1$ m/s².

$80\eqslantless{}t\eqslantless{}120,$ $a_2=\frac{0-20}{40}=-0.5$ m/s².

$150\eqslantless{}t\eqslantless{}160,$ $a_3=\frac{-10-0}{10}=-1$ m/s².

$190\eqslantless{}t\eqslantless{}200,$ $a_4=\frac{0-(-10)}{10}=1$ m/s².