an athlete runs at a distance of 1500m in the following manner:1.starting from the rest he acceralate himself uniformly 2m/s*s till he covers a distance of 900m 2.he then runs the remaining distance of 600m at the uniform speed developed
Calculate the time taken by the athlet to cover the two parts of distance covered,also find the time when he is at the centre of the track
1500 m races are run on oval tracks, not straight line tracks. Runners do not move toward the "center of the track". Perhaps they want the time when the distance covered is 750 m.
The speed reached during the first part would be
V = sqrt(2aX) = 60 m/s
It would take him V/a = 30 s to reach that speed.
The last 600 m would be run in 600/60 = 10 s.
No one can run that fast. A champion distance runner will reach a peak speed of about 8 m/s.
This is a very unrealistic problem.
To find the time taken by the athlete to cover each part of the distance, we can use the formulas of motion.
1. Accelerated Motion:
In the first part, the athlete accelerates uniformly. We are given the initial velocity (u = 0 m/s), final velocity (v, which we need to find), and acceleration (a = 2 m/s²).
The formula connecting these quantities is:
v = u + at
We can rearrange this equation to solve for v:
v = u + at
v = 0 + 2 × t
v = 2t
Since the distance covered is 900m, we can use the formula:
distance = (u + v) × t / 2
Substituting the values:
900 = (0 + 2t) × t / 2
900 = t²
Solving for t:
t = √900
t = 30 seconds
So it takes the athlete 30 seconds to cover the first 900 meters.
2. Constant Speed Motion:
In the second part, the athlete runs at a constant speed. We are given the distance (600m) and the speed (which we need to find).
The formula connecting distance, speed, and time is:
distance = speed × time
Substituting the values:
600 = speed × time
Since we already found the time taken in the first part to be 30 seconds, we can substitute this value:
600 = speed × 30
Solving for speed:
speed = 600 / 30
speed = 20 m/s
So the speed at which the athlete runs the remaining distance of 600m is 20 m/s.
To find the time when the athlete is at the center of the track, we need to consider the average speed of the entire distance covered.
Total distance = 1500m
Total time = time taken in the first part + time taken in the second part
Total time = 30s + 600m / 20m/s
Total time = 30s + 30s
Total time = 60 seconds
Therefore, the time when the athlete is at the center of the track is 60 seconds.