Calculating Acceleration, Displacement for 100m Sprint

In summary, the problem involves a runner starting from rest and accelerating to 9.6 m/s [W] in 4.2 seconds. The acceleration is 2.3 m/s^2 [W] and the displacement is 20.16 m [W]. To find the total time, the distance of 100 m is subtracted by the displacement of 20.16 m, giving 80 m. This distance is then divided by the constant velocity of 9.6 m/s [W] and added to the initial time of 4.2 seconds, resulting in a total time of 13 seconds.
  • #1
Veronica_Oles
142
3

Homework Statement


In a 100 m sprint a runner starts from rest and accelerate to 9.6 m/s [W] in 4.2 s.
Calculate acceleration, displacement, and if the runner runs at a constant velocity for the rest of the race what is the total time?

Homework Equations

The Attempt at a Solution


I am having trouble with the total time. I know acceleration is 2.3 m/s^2 [W] and I know displacement is 20.16 m [W]. However what would the constant velocity be.. Is it 9.6 m/s[w]? And since it states the rest of the race does that mean i have to subtract 20.16 from the 100m?
 
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  • #2
Veronica_Oles said:

Homework Statement


In a 100 m sprint a runner starts from rest and accelerate to 9.6 m/s [W] in 4.2 s.
Calculate acceleration, displacement, and if the runner runs at a constant velocity for the rest of the race what is the total time?

Homework Equations

The Attempt at a Solution


I am having trouble with the total time. I know acceleration is 2.3 m/s^2 [W] and I know displacement is 20.16 m [W]. However what would the constant velocity be.. Is it 9.6 m/s[w]? And since it states the rest of the race does that mean i have to subtract 20.16 from the 100m?
So what I did was take 100 subtract 20 to obtain 80. Then I took 80 divided it by 9.6 took that number and added 4.2 seconds to get the total time. The total time is 13s.. Can someone tell me if I did this correctly?
 
  • #3
Veronica_Oles said:
So what I did was take 100 subtract 20 to obtain 80. Then I took 80 divided it by 9.6 took that number and added 4.2 seconds to get the total time. The total time is 13s.. Can someone tell me if I did this correctly?
Looks good.
 

1. How do you calculate acceleration for a 100m sprint?

Acceleration is calculated by dividing the change in velocity by the change in time. In the case of a 100m sprint, the initial velocity is 0m/s and the final velocity is the speed at the finish line. The time can be measured using a stopwatch or timing device. The formula for acceleration is: acceleration = (final velocity - initial velocity) / time

2. What is the average acceleration for a 100m sprint?

The average acceleration for a 100m sprint can vary depending on the runner's speed and technique. However, on average, a sprinter can achieve an acceleration of 9.8 m/s², which is equal to the acceleration due to gravity. This means that for every second of the race, the sprinter is increasing their speed by 9.8 meters per second.

3. How do you calculate displacement for a 100m sprint?

Displacement is the change in position of an object. In a 100m sprint, the displacement is the distance between the starting point and the finish line. This can be calculated by measuring the length of the race track or by using the formula: displacement = final position - initial position In this case, the initial position is 0m and the final position is 100m.

4. Is displacement the same as distance in a 100m sprint?

No, displacement and distance are not the same. Distance is the total amount of ground covered, while displacement is the change in position. In a 100m sprint, the distance may be longer than 100m if a runner takes a curved path, but the displacement will still be 100m as it only measures the change in position.

5. How can you use acceleration and displacement to improve a 100m sprint time?

By understanding the relationship between acceleration and displacement, a sprinter can work on improving their speed and technique to decrease their time. A higher acceleration can lead to a shorter displacement, meaning the runner covers more ground in less time. Additionally, focusing on improving acceleration in the first few seconds of the race can lead to a faster overall time.

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