Speed,Time and Distance

Speed

Speed is the total distance covered by an object in unit time interval .It is obtained by dividing distance covered by the time to cover the distance.

Speed=Distance Travelled /Time taken

Also,
distance = Speed x Time taken

Time Taken = Distance travelled / Speed

Here, the unit of speed are km/h,m/s etc.

Average Speed

Average Speed is the ratio of total distance covered to total time taken to cover the distance.


Relative Speed

When two object are moving , then you have to take into consideration their relative speed in place pf their individual speeds. Relative speed is the Speed of one object with respect to other.

CASE 1:- 

x km/h
A------→

x m/s
B-----→
when two object are moving in the same direction with x km/h and y km/h respectively.
Relative speed = (x-y) km/h
                          (y-x) m/s
CASE 2:-

x km/h
A→

y km/h
←B
when two objects are moving  in the opposite direction with x km/h and y km/h respective, then 
Relative Speed = (x+y) km/h

Rules Related to Moving Objects

RULE:- 
              when a person travels a distance at speed of x km/h and return the same distance at speed of y km/h , then the average speed is given by 

RULE :- 
              When a person travels a certain distance with a speed of x1 km/h and then further the same distance with a speed of x2 km/h then further the same speed x3 km/h and so on. Then average speed of the complete journey is given by

RULE :- 
              when a person travels d1 distance at a speed of x1 km/h , d2 distance at a speed of x2 km/h and d3 distance at a speed of x3 km/h and so on . Then average speed of the journey is given by

RULE :- 
             when a person change his speed to (x/y) of its usual speed and reaches early by a min,then usual time taken by the person to reach his destination.
is

Problem Based on Trains

In problem based on train , the concept used is same as that of speed and time except the length of train is taken into account . Following points will help a student to understand the concept better:

1 Train Vs Stationary object on no length :- Time taken by a train of length l m to pass a stationary object such as a pole , standing man or a building is equal to the time taken by the train to cover l m
        Speed of train 
                               =


 2. Train vs Stationary object of certain length:-  Time taken by a train of 'l' m to pass a stationary object of length 'a' m (such as, another standing train, bridge or railway platform) is equal to the time taken by the train to cover the distance (l + a)m.





3. Train vs moving object of no length :- Time taken by a train of length l m to pass a man moving is equal to the time taken by the train to cover l m.

(i) When the train and a man move in the same direction with the speeds x m/s and y m/s respectively.

 (ii) when the train and a man move in the opposite directions with the speeds x m/s and y m/s  respectively.
4. Train vs Moving object of certain length :-  Time taken by the train of length l m to pass a moving object of length a m (such as another moving train) is equal to the time taken by the train to cover the distance (l+a) m.

(i) When two trains move in the same direction with the speeds x m/s and y m/s respectively, where x > y then

(ii) When two trains move in the opposite directions with the speeds x m/s and y m/s , respectively.
(iii) When two trains of lengths a m and b m are moving in the same direction or opposite directions with the speeds x and y m/s respectively (where x > y), then time taken to cross each other is:-


Concept of boat and streams

The basic  concept of boats and streams include the following terminologies:
        1. Downstream motion :- When an object is moving in the direction in which the stream of water is flowing, then the object is said to be moving downstream.
        
        2. Upstream motion:- When an object is moving against (opposite) the direction in which the stream of water is flowing , then the object is said to be moving upstream.

        3. Motion in still water :- When an object is moving in water, when there is no motion in water, the object can move in any direction with a uniform speed , then the object is said to be moving in still water.
    
        4. Downstream and upstream speed :- let the speed of the boat in still water be x km/h and speed of the stream be y km/h, then,



 As, when the boat is moving downstream, the speed of the water aids the speed of the boat and when the boat is moving upstream , the speed of the water reduces the speed of the boat.



Solved Example

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More Practice Problem on Speed, time and Distance
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Solution of Practice sheets
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