## 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 **

**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 :- **

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= s1–s2

**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= s1–s2

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.

**Upstream****: **While 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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