Time and Distance

Time and Distance:
Speed = Distance / Time
Average = Total distance travelled/ total time taken

If two bodies are moving in the same direction , then their relative velocity or the speed by which they will overtake one another is equal to the difference of their speeds u- v kmph. If they are travelling in opposite directions then their relative velocity is u + v kmph.

Problems based on trains:
i) When the train, crosses telephone post or a tree, the train will move a distance equal to the length of the train. Therefore, the time taken by a train to cross a tree = length of the train/ Speed of the train

ii) When a train crosses the bridge or a platform the train will have to travel a distance equal to the sum of the lengths of the bridge and train , thus, time taken by train to cross a platform = length of the train + length of the platform / Speed of the train

iii) If two trains a and B are running in the same direction , then the relative speed of the faster train A with respect to the slower train B is the difference between the speeds of the faster train A and the slower train B.

Then the time in which the trains will cross each other is the time taken by the faster train A covering a distance equal to the sum of the lengths of the trains with respect to the relative speed.
Thus, the time taken by the slower train to catch the faster train =
Distance covered in extra time / Difference in Speeds

Time taken to cross each other =
Sum of the lengths of both the trains/ Difference of their speeds

iv) If two trains are running in opposite directions , then the relative speed of the faster train A with respect to the slower train B is the sum of the speeds. They will cross each other at a time equivalent to the time taken in travelling a distance equal to the sum of the lengths of the trains with respect to the relative speed
The time taken to touch each other = Difference in lengths/ Sum of speeds

Time taken to cross each other = sum of lengths/ sum of speeds

v) When a train crosses a man who is walking, two situations arise:
I : when they are moving in the same direction, then the relative speed of the train with respect to the man = Speed of Train - Speed of Man
II: when they are moving in the opposite directions:
Speed of Train + Speed of Man

Rowing Upstream and Downstream:
If a man rows a boat at A kmph in still water and B kmph be the velocity of the current , then the man will row his boat with velocity (a + b) kmph and (a-b) kmph downstream and upstream respectively

Speed of the boat in Downstream direction:
= speed of the boat in still water + speed of the stream.
Speed of the boat in Upstream direction:
= speed of the boat in still water - speed of the stream

Speed of the stream = speed of boat downstream – speed of boat in upstream / 2
Speed of boat in still water = speed of boat downstream + speed of boat in upstream / 2