One simple model for a person running the 100m dash is to assume the sprinter runs with constant acceleration until reaching top speed,then maintains that seed through the finish line.if sprinter reaches his top speed of 11.1m/s in 2.54s. What will be his total time?
V = a*t = 11.1 m/s.
a*2.54 = 11.1.
a = 4.37 m/s^2.
d1 = 0.5a*t^2 = 0.5*4.37*2.54^2 = 14.1 m
d2 = V*t = 100-14.1.
11.1*t = 85.9.
t = 7.74 s.
2.54 + 7.74 = 10.3 s. = Total time.
To find the total time for the sprinter to complete the 100m dash, we need to consider two parts:
1. The time it takes for the sprinter to reach their top speed.
2. The time it takes for the sprinter to maintain their top speed until the finish line.
Let's break down the problem step by step.
Step 1: Finding the time to reach top speed
Given:
- Initial speed (u) = 0 m/s (since the sprinter starts from rest)
- Final speed (v) = 11.1 m/s
- Acceleration (a) = ?
We can use the formula v = u + at, where:
- v is the final speed
- u is the initial speed
- a is the acceleration
- t is the time taken
Rearranging the formula to solve for time (t), we get:
t = (v - u) / a
Substituting the values, we have:
t = (11.1 m/s - 0 m/s) / a
t = 11.1 m/s / a
Step 2: Finding the time to cover the remaining distance
Since the sprinter has already reached their top speed, we can assume they maintain that speed until the finish line. The time it takes to cover a distance when moving at a constant speed is given by the formula:
t = d / v
where:
- d is the distance
- v is the velocity or speed
Given:
- Distance (d) = 100 m
- Speed (v) = 11.1 m/s
Substituting the values, we have:
t = 100 m / 11.1 m/s
Step 3: Calculating the total time
To find the total time, we add the time to reach top speed (Step 1) to the time to cover the remaining distance (Step 2).
Total Time = Time to reach top speed + Time to cover the remaining distance
Total Time = t + t
Total Time = 11.1 m/s / a + 100 m / 11.1 m/s
Simplifying further, we get:
Total Time = 2.54 s + 9.01 s
Total Time = 11.55 s
Therefore, the sprinter's total time to complete the 100m dash using this model would be approximately 11.55 seconds.