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 A and B stand at distinct points of a circular race track of length 135 m. They cycle at a speed of a m/s and b m/s. They meet for the first time 5 secs after they start the race.
A and B stand at distinct points of a circular race track of length 135 m. They cycle at a speed of a m/s and b m/s. They meet for the first time 5 secs after they start the race.
Solve circular race track dynamics with distinct starting points and varying speeds. Discover how A and B's meeting times change with different initial directions.
by Maivizhi A
Updated Mar 18, 2024
A and B stand at distinct points of a circular race track of length 135 m. They cycle at a speed of a m/s and b m/s. They meet for the first time 5 secs after they start the race and for the second time 14 seconds from the time they start the race. Now if B had started in the opposite direction to the one he had originally started. They would have met for the first time after 60 seconds. If B is quicker then A, then find b?
b = 8 m/s.
Here's how
First Meeting after 5 seconds: When they meet for the first time after 5 seconds, the total distance covered by A and B combined is equal to the circumference of the circular track, which is 135 meters.
So, we have the equation:
"5a + 5b = 135" [since distance = speed × time]
Second Meeting after 14 seconds: When they meet for the second time after 14 seconds, A has covered one lap more than B. The difference in the distances covered by A and B in 14 seconds would be one lap.
So, we have the equation:
"14a  14b = 135" [same logic as above]
Meeting after 60 seconds in opposite directions:
When they meet for the first time after 60 seconds while moving in opposite directions, the relative speed is the sum of their individual speeds.
So, we have the equation:
"60(a+b) = 135"
Now, we can solve these equations to find the value of 'b'.
From equation (1):
"5a + 5b = 135"
"a + b = 27"
From equation (2):
"14a  14b = 135"
"a  b = 135/14"
Now, solving these two equations simultaneously:
"a + b = 27"
"a  b = 135/14"
Adding the two equations, we get:
"2a = 27 + 135/14"
"2a = (378 + 135)/14"
"2a = 513/14"
"a = 513/28"
Now, substituting the value of 'a' into equation (1):
"(513/28) + b = 27"
"b = 27  (513/28)"
"b = (756  513)/28"
"b = 243/28"
Thus, "b = 243/28 ≈ 8.68" meters per second.
Time, Distance and Speed
Time, distance, and speed are interconnected concepts in physics and mathematics that are fundamental to understanding motion and travel. Here's a brief overview of each:

Time: Time is a measure of the duration between events. It's often denoted in units such as seconds, minutes, hours, days, etc. Time is a continuous and unidirectional dimension that flows uniformly forward (according to conventional understanding).

Distance: Distance is a measure of the length between two points. It can be measured in various units such as meters, kilometers, miles, etc. Distance is also a continuous dimension but is not inherently directional; it simply describes the extent of space between two objects or points.

Speed: Speed is a measure of how quickly an object moves through space. It's typically measured in distance units per unit of time, such as meters per second (m/s), kilometers per hour (km/h), miles per hour (mph), etc. Speed indicates the rate of change of distance with respect to time.
These concepts are related by the following formula:
Speed = Distance / Time
This formula can be rearranged to solve for any of the three variables if the other two are known.
 If you know the speed and the time, you can find the distance traveled using the formula: Distance = Speed * Time
 If you know the distance and the time, you can find the speed using the formula: Speed = Distance / Time
 If you know the distance and the speed, you can find the time using the formula: Time = Distance / Speed
Understanding these concepts and relationships is crucial for solving problems involving motion, such as calculating travel times, determining vehicle velocities, or estimating arrival times.
A and B stand at distinct points of a circular race track of length 135 m. They cycle at a speed of a m/s and b m/s. They meet for the first time 5 secs after they start the race and for the second time 14 seconds from the time they start the race  FAQs
1. What is the circular race track problem about?
The problem involves two cyclists, A and B, starting from different points on a circular track, meeting at various intervals, and determining their speeds.
2. How do we calculate the distance covered by A and B in the circular race track problem?
We use the formula: distance = speed × time. In this scenario, the total distance covered by A and B is equal to the circumference of the circular track.
3. What equations are derived from the first meeting of A and B?
The equation "5a + 5b = 135" is derived, representing the total distance covered by A and B in 5 seconds.
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