Question

a train starting from rest picks up a speed of 20m/s in 200 seconds . it continues to move at the same speed for the next 500 seconds . it is then brought to rest next 100 seconds.
1. plot a speed time graph
2.calculate the rate of uniform acceleration.
3.calculate the distance covered by the train during retardation
4. calculate the average speed during retardation.

Answer 1

Question#11369

a train starting from rest picks up a speed of $20\mathrm{m/s}$ in 200 seconds. It continues to move at the same speed for the next 500 seconds. It is then brought to rest next 100 seconds.

1. plot a speed time graph

2. calculate the rate of uniform acceleration.

3. calculate the distance covered by the train during retardation

4. calculate the average speed during retardation.

Solution:

Let:

$$\begin{array}{l} v0 = 0 \\ v1 = 20\mathrm{m/s} \\ t1 = 200\mathrm{sec} \\ t2 = 500\mathrm{sec} \\ t3 = 100\mathrm{sec} \\ \end{array}$$

1

2.

$$a = \frac{v1 - v0}{t1} = \frac{20}{200} = 0.1\mathrm{m/sec^2}$$

3.

$$S = v1 * t3 + \frac{a1 * (t3)^2}{2} = v1 * t3 + \frac{\frac{v0 - v1}{t3} * (t3)^2}{2} = v1 * t3 - \frac{1}{2} v1 * t3 = \frac{1}{2} v1 * t3$$ $$S = \frac{1}{2} 20 * 100 = 1000\mathrm{m}$$

4.

$$v(average) = \frac{v1 - v0}{2} = \frac{20}{2} = 10m/sec$$