Speed Time and Distance Notes

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Formulas

Basic formulae for speed time and distance notes

Speed Time and Distance Notes

SPEED:-  Distance travelled by any body w.r.t. Time is known as speed.
Pictorial diagram to remember these formulae  
Trick to remember Formulas

Conversion of Units:-
1 km/hr = 5/18 m/s
X km/s = (5 /18) X m/s
1 m/s    = 18/5 km/ hr
 X km/hr = ( 18/5) km/hr

Basic Rules :-

Basics Rule

figure: Speed Time and Distance Notes relations while one quantity is constant where k is constant.


Example:- A car travels at 60 km/hr for the first 3 hrs & then 80 km/hr for the next 3 hrs. Find the      ratio of distance travelled
Solution:-
d1/d2=s1/s2= 60/80 = ¾

Relative Speed:Relative speed is the speed when one moving body relative to another moving body.when both bodies are moving in same direction the speeds are subtracted and when both bodies are moving in opposite  direction the speeds are add up.
Case 1:
Two bodies are moving in opposite directions at speed s1 & s2 respectively. The relative speed is defined as sr=s1+s2
Case 2:
Two bodies are moving in same directions at speed s1 & s2 respectively. The relative speed is defined as sr= s1s2

Average speed:-
The average speed of an object is the total distance traveled by the object divided by the elapsed time to cover that distance.
 Average speed = Total Distance / Total Time

Meeting Point:-
 M.p. = Initial distance between two bodies/Their relative speed
Rule:- A and B moving towards each other from two end  of the journey points , take time in the ratio b:a after crossing to reach  opposite end the, ratio of speed
Sa/Sb =(b/a)^1/2

TRAINS
Speed = Distance/Time
When the train is crossing a moving object, the speed has to be taken as the relative speed of the train with respect to the object.
sr=s1+s2 or  sr= s1s2
The distance to be covered when crossing an object, whenever trains crosses an object will be equal to: Length of the train + Length of the object ( e.g. Train,Pole,Platform or Man)

BOATS AND STREAMS  
Upstream:- If a person or boat moves against the stream, it is called upstream.
Downstream:- If a person or boat moves with the stream, it is called downstream.
Assumption:-  When we simply say speed of the person or boat ,it usually means speed in still water.  Let,
B = Velocity of the boat in still water
S = Velocity of the stream.

UpstreamWhile moving in upstream

Speed (U) =  (B – S) Km/hr

Downstream: In case of downstream

Speed (D) =  (B + S) Km/hr
Speed of boat in still water = ½ [  D+U ]
Speed of the stream = ½ [ D-U ]

RACES AND GAMES
Races: A contest of speed in running, riding, driving, sailing or rowing is called a race.
Race Course: The ground or path on which contests are made is called a race course.
Starting Point: The point from which a race begins is known as a starting point.
Winning Point or Goal: The point set to bound a race is called a winning point or a goal.
Dead Heat Race: If all the persons contesting a race reach the goal exactly at the same time, the race is said to be dead heat race.
Start: Suppose A and B are two contestants in a race. If before the start of the race, A is at the starting point and B is ahead of A by 20 metres, then we say that ‘A gives B, a start of 20 metres’.
To cover a race of 100 metres in this case, A will have to cover 100 metres while B will have to cover only (100 – 20) = 80 metres.
In a 100 race, ‘A can give B 20 m’ or ‘A can give B a start of 12 m’ or ‘A beats B by 20 m’ means that while A runs 100 m, B runs (100 – 20) = 80 m.
Games: ‘A game of 100, means that the person among the contestants who scores 100 points first is the winner’.
If A scores 100 points while B scores only 80 points, then we say that ‘A can give B 20 points’.
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