Math Formulas: Problems on Speed, Time and Distance

1. km/hr to m/s conversion:
    a km/hr = a x (5/18) m/s
2. m/s to km/hr conversion:
    a m/s = a x (18/5)km/hr

 Formulas for finding Speed, Time and Distance

1. Time taken by a train of length l meters to pass a pole or standing man or a signal post is equal to the time taken by the train to cover lmeters.
2. Time taken by a train of length l meters to pass a stationery object of length b meters is the time taken by the train to cover (l + b) meters.
3. Suppose two trains or two objects bodies are moving in the same direction at u m/s and v m/s, where u > v, then their relative speed is = (u - v) m/s.
4. Suppose two trains or two objects bodies are moving in opposite directions at u m/s and v m/s, then their relative speed is = (u + v) m/s.
5. If two trains of length a meters and b meters are moving in opposite directions at u m/s and v m/s, then: 
   The time taken by the trains to cross each other = (a + b)/(u + v) sec
6. If two trains of length a meters and b meters are moving in the same direction at u m/s and v m/s, then: 
   The time taken by the faster train to cross the slower train = (a +b)/(u - v) sec
7. 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 sec in reaching B and A respectively, then:
   (A's speed) : (B's speed) = (√b : √a)