Question

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

Answer 1

Question 37237

a)

b)

I. $S = \frac{1}{2} \cdot 20 \cdot 20 + 60 \cdot 20 + \frac{1}{2} \cdot 40 \cdot 20 = 1800 \, \text{m}$ (These are the sums of the areas on the graph from $t = 0$ to $t = 120$ )

II. Since the train was at rest from point C till point B, the displacement remains the same - $S = 1800 \, \text{m}$ .

III. For:

$$0 < t < 20, \quad a = \frac{20 \frac{\text{m}}{\text{s}}}{20 \text{s}} = 1 \frac{\text{m}}{\text{s}^2}$$ $$80 < t < 120, \quad a = \frac{-20 \frac{\text{m}}{\text{s}}}{40 \text{s}} = -0.5 \frac{\text{m}}{\text{s}^2}.$$