TIME, WORK AND DISTANCE
There is a definite relation between time, work and distance. Well known rela- tions between these three quantities are
Speed = distance
time
or distance = speed C time
1 km / hr = 5 m / s
18
or 1 m / s = 18 km / hr
5
Similarly velocity = displacement
time
or displacement = velocity C time velocity and displacement both are vector quantities means they have both magnitude and direction, while distance and speed are scaler quanties means they have only magnitude.
IMPORTANT POINTS TO REMEMBER
- If A can do a work in x days, the work done
by A in one day= 1 .
x
- If A’s 1 day’s work = 1, then the time taken by A to do the work = x days.
x
- In a storage tank, the pipe which fills it is called an inlet pipe while the pipe that empties it is called as an outlet
- If an inlet pipe fills a tank in n hours, then the work done by it in 1 hour
= 1 .
n
- If an outler pipe empties a tank in x hours, then the work done by it in 1 hour
= -1 .
x
TIME AND DISTANCE
Uniform speed : If a body covers equal distances in equal intervals of time, its speed is said to be uniform.
Relative speeds : 1. If two bodies are moving in opposite direction with speed x km/hr and y km/hr respectively, then (x + y) km/hr is known as their relative speed.
- If two bodies are moving in same direction with speed x km/hr and y km/hr respectively then (x – y) km/hr is called their relative This is applicable in case of boat and river.
- Relative speed of two bodies in same direction is (x – y) km/hr.
- Relative speed of two bodies in opposite direction is (x + y) km/hr.
SOME POINTS TO SOLVE THE PROBLEMS
(A) If a train of length 1 metres is moving at x km/hr, then
- the time which the train takes to cover a stationary object is the time taken by the train to cover 1 metres at x km/hr.
- the time which the train takes to cover a stationary object (of length b) is the time which the train takes to cover (1+b) metres at x km/hr.
- If the two trains of length I metres and b metres are travelling in opposite directions with a speed of x km/hr and y km/hr respectively, then the time taken by total to cross each other is the time taken to cover (1+b) metres with the relative speed (x+y) km/
- i.e. time = (1+b)
(x+y)
- If two trains of length 1 metres and b metres are travelling in the same direction with a speed of x km/hr and y km/hr respectively when x — y, then, the time taken by faster train to cross the slower train is the time taken to cover (1+b) metres at a relative speed of (x – y) km/hr e. time
= (1+b)
(x-y)
- The time taken by a train of length 1 metres moving at x km/hr to cross a man running at y km/hr.
- in the same direction, is the time taken to cover 1 metres distance with a speed of (x – y) km/hr. i.e.
time = 1 .
x – y
- in the opposite direction, is the time taken to cover 1 metres distance with a speed of (x – y)
km/hr. i.e. time 1 .
x + y
Problems of relative speeds are of great importance in physics. Relativity is mainly based on relative speeds. Relativestic mechanics is one important branch of mathematics.
