TIME,SPEED AND DISTANCE

                           Time, Speed and Distance

 

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

 

Properties of time and distance:

=>Distance travelled is proportional to the speed of the object if the time is kept constant.

=>Distance travelled is proportional to the time taken if speed of 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 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

*km/hr to m/sec conversion:

 x km/hr = [x * (5/18)]m/sec

*m/sec to km/hr conversion:

 x m/sec = [x * (18/5)]km/hr

Example sum

A van covers a distance of 690Km 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 same direction with speeds of x and y then their relative speed is x-y

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

 

ex: Two trains in opposite directions at 36kmph and 45kmph and a man sitting in --- slower train passes the faster train in 8 seconds. Find the length of the faster     train?

sol: relative speed = (36 + 45)km/hr

---                 = 81 km/hr

                                  =81 * (5/18) m/sec

                                  =(45 / 2) m/sec

     length of the train = (45/2) *8m

                                              =180m

 

Basic Formulas

=>If some distance is travelled at x km/hr and the distance is travelled at y km/hr

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

=>When you are given two different speeds (s1 and s2) for travelling through a certain distance, and total time (t) for these two journeys:

 Distance = [(s1 * s2) / (s1 + s2)]*t

=>When you are given two different speeds (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 - s1)]*t

 

examples

1)A person travels from A and 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?

sol: 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

2)A boy goes from A to B at 3km/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:

sol: Distance = (product of speeds / addition of speeds) *time

              = [(3*2) / (3+2)] *5

              = [6/5]*5

              = 6km