## Problems on Trains

### Introduction

1. a km/hr  = $$\left(a \times \frac{5}{18}\right)$$ m/s
2. a m/s = $$\left(a \times \frac{18}{5}\right)$$ km/hr
3. Time is taken by a train of length I metres to pass a pole or a standing man or a signal post is equal to the time taken by the train to cover 1 meter
4. Time is taken by a train of length 1 metres to pass a stationary object of length b metres is the time taken by the train to cover (I+b) meters
5. Suppose two trains or two bodies are moving in the same direction at u m/s and v m/s,  where u>r, then their relative's speed =(u-w)
6. Suppose two trains or two bodies are moving in the opposite directions at u m/s and v m/s then their relative speed is = (u + v ) m/s

### Important Facts

If two trains of length metres and b metres are moving in opposite directions at u m/s and v m/s, then the time taken by the trains to cross each other = $$\frac{(a+b)}{(u+v)}$$ sec

If two trains of length metres and b metres are moving in the same direction at u m/s and v m/s then the time is taken by the faster train to cross the slower train = $$\frac{(a+b)}{(u-v)}$$ sec

If two trains (or bodies). start at the same time from points A and B towards each other and after crossing they take a and b to see in reaching B and A respectively, then (A's speed) : (B's speed) = $$(\sqrt{b} : \sqrt{a})$$