Time and Distance

Time and Distance
Time and distance are related to the speed of a moving object.


Properties of Time and Work
• Distance traveled is proportional to the speed of the object if the time is kept constant.
• Distance traveled is proportional to the time taken if the speed of the object is kept constant.
• Speed is inversely proportional to the time taken if the distance covered is kept constant.
• If the ratio of two speeds for the same distance is a:b then the ratio of time taken to cover the distance is b:a


Speed
Speed is defined as the distance covered by an object in unit time.

Basic Formulas

Speed = ( Distance / Time )Distance = Speed * Time
Time = ( Distance / Speed )

Example sum 
A van covers a distance of 690 km in 30h. What is the average speed of the car?
Speed = ( Distance / Time )
= 690 / 30
= 23 km/h

Relative Speed
If two objects are moving in the same direction with speeds of x and y then their relative speeds (x - y)

If two objects are moving in the opposite direction with speeds of x and y then their 
relative speed is ( x + y )


Example sum
Two trains travel in opposite directions at 36 kmph and 45 kmph and a man sitting in slower train passes the faster train in 8
seconds. Find the length of the faster train?
Relative Speed = ( 36 + 45 ) km/hr
= 81 km/hr

= 81*(5/18) m/sec = (45/2) m/sec
Length of the train = ( 45 /2) *8 m
= 180 m
Basic Formulas

If some distance is traveled at x km/hr and the same distance is traveled at y km/hr

Average speed of the whole journey
=[(2xy ) / (x + y) ] kmph

Example sum

A person travels from A to B at a speed of 40 km/hr and returns by increasing his speed by 50%. What is his average speed

for both the trips?

Speed with which he travels from A to B =40 km/hr

Speed with which he travels from B to A =

[40*(100+50)/100]

= 60 km/hr

Average speed = (2 * 40 * 60 ) / ( 40 + 60)

= 48 km/hr

Basic Formulas

When you are given two different speeds (s1 and s2) for traveling through a certain distance, and total time (t) for these two

journeys:

Distance = [ (s1*s2) / (sl +s2 ) ]*t

Example sum

A boy goes from A to B at 3 km/hr,back from B to A at 2 km/hr.Total time for these two journeys is 5 hours, then

distance from A to B is given by:

Distance = ( Product of speeds / Addition of speeds ) * Time

Distance= [(3*2)/(3+2)]*5
= [ 6/5]*5
= 6 km

Basic Formulas

When you are given two different speed  (s1 and s2) for  travelling through a certain distance, and total difference in time (t) is

given for these two journeys: Distance = [ (s1*s2)/(s2 - sl ) ] *t  

Example sum

A boy goes from A to B. If speed is 30km/hr ,he is late by 10 minutes. If speed is 40 km/hr,he reaches 5 minutes earlier, then distance from A to B is given by?

Difference in time = 10 - (-5) [ earlier 5 min = (-5) ]

= 15 minutes

= (15/60) hr

= 1/4 hr

Distance = ( Product of speed / Difference of speed ) * Difference in time
= [(30 * 40)/(40-30)]*(1/4)
= (1200/10)*(1/4)
= 120*(1/4)

= 30 km