Question

what is
>Average speed
>Relative speed
>Travel and meeting problems
>Boats and stream problems
>Races
>Circular Track
​

Answer 1

Step by step explanation:

Average Speed:

• When a body travels different distances at different speeds, the average speed is the amount of time taken to travel the total distance in total time, Therefore, the formula for Time Speed Distance is:

• A.S = T.D/T.T

• When the body travels at speeds of u and v units for equal distances, i.e. the distance segments are in the ratio 1:1, then

• A.S = 2uv/u+v

Relative speed :

Consider two bodies moving at speeds u and v.

• When they are moving in the same direction, the relative speed between the two bodies is the difference of their speeds, i.e.u – v if u > v or v – u if v > u.
• When they are moving in the opposite directions, the relative speed between the two bodies is the sum of their speeds, i.e. u + v

Travel and meeting:

• When two persons start from two points at the same time and travel towards each other, the time taken by each of them to reach the meeting point is the same. Hence, the distances covered by them from their respective starting points to the meeting point will be proportional to their respective speeds.

• D1/d2 = S1/s2

Boats and stream problems:

• The two quantities that come into the picture are the speed of the stream or river or current, and the speed of the boat or swimmer in still water.
• When the boat is moving against the current, it is said to move ‘upstream’. Then the effective speed at which it moves is the difference between its speed in still water and the speed of the current.
• When the boat is moving with the current, it is said to move ‘downstream’. Then the effective speed at which it moves is the sum of its speed in still water and the speed of the current.
• If u and v are the upstream and downstream speeds of the boat, then
• Speed of the boat in still water = (u + v)/2
• Speed of the stream = (v - u)/2

Races:

• A race involves runners covering a certain distance and the person who reaches the finishing point first wins the race. A ‘kilometer race’ requires the participants to run for 1 km. Unless otherwise specified, a race is assumed to be run on a linear track. A race can also be run on a circular track.

• Suppose two runners A and B run a race.
• If A reaches the finishing point first and B is still behind by ‘x’ meters, A is said to win the race by ‘x’ metes. In this case, both ran for equal amounts of time but only A ran the whole distance.

• If A reaches the finishing point first and B needs ‘t’ more minutes to complete the race, A is said to win the race by ‘t’ minutes. In this case, both ran for equal distances but B took more time than A.
• If B starts running only ‘t’ minutes after A has started, A is said to have a start of ‘t’ minutes.
• If B starts running only after A has covered ‘x’ meters, A is said to have a start of ‘x’ meters.

Circular tracks:

• Circular tracks may involve two or three participants. They usually start from the same point and run in the same or opposite directions. Let the length of the track by ‘l’ metres.
• When two runners start from the same point and run in opposite directions with speeds ‘a’ and ‘b’ m/s, the following points apply
• Their relative speed is equal to the sum of their individual speeds.
• Between any two meetings, the total distance covered by them together is equal to the length of the circular track.
• Time taken for the first meeting after starting = d/s = l/(a + b)
• Time taken for them to meet at the starting point for the first time = LCM of (l/a) and (l/b)

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