Circular Track Meeting Time Calculation
This problem involves calculating the time it takes for two runners, moving in opposite directions on a circular track, to meet for the first time. We can solve this using the concept of relative speed.
Key Information
- Track Length = 400 meters
- Speed of Runner A ($v_A$) = 6 m/s
- Speed of Runner B ($v_B$) = 4 m/s
- Direction: Opposite
Relative Speed Concept
When two objects move in opposite directions, their relative speed is the sum of their individual speeds. This is the speed at which the distance between them decreases.
Relative Speed ($v_{rel}$) = $v_A + v_B$
In this case, $v_{rel} = 6 \text{ m/s} + 4 \text{ m/s} = 10 \text{ m/s}$.
Calculating Meeting Time
For the runners to meet for the first time, the total distance covered by both combined must equal the length of the circular track.
Time = Total Distance / Relative Speed
Time = $\frac{\text{Track Length}}{v_{rel}}$
Time = $\frac{400 \text{ meters}}{10 \text{ m/s}}$
Time = 40 seconds
Conclusion
The runners will meet for the first time after 40 seconds.
Important Questions from Speed Time and Distance
A journey of 900 km is completed in 11 h. If two-fifth of the journey is completed at the speed of 60 km/h, at what speed (in km/h) is the remaining journey completed?
A car starts from point A towards point B, travelling at the speed of 20 km/h. 1 \(\frac{1}{2}\) hours later, another car starts from point A and travelling at the speed of 30 km/h and reaches 2 \(\frac{1}{2}\) hours before the first car. Find the distance between A and B.
A bus covered a distance of 162 km. If speed of this bus is 15 m/s, then what will be the time taken ?
An athlete runs an 800 m race in 96 seconds. His speed (in km / h) is:
A person has to cover a distance of 150 km in 15 hours. If he traveled with the speed of 11.8 km/hr for 10 hours. At what speed he has to travel to cover the remaining distance in the remaining time?
