Acceleration of a runner to finish in his desired time

In summary, a runner wants to complete a 10,000 meter run in less than 30 minutes, and after 25 minutes has passed, there are 1900 meters left to go. In order to achieve the desired time, the runner must accelerate at a rate of 0.22 m/s^2 for a certain amount of time. Using the SUVAT equations, the time needed can be calculated by using the initial velocity of 5.4 m/s, the distance remaining, and the given acceleration.
  • #1
Pioneer98
19
0

Homework Statement



A runner hopes to complete the 10,000 meter run in less than 30 minutes, after exactly 25 minutes there are 1900 meters to go. The runner must then accelerate at 0.22 m/s^2 for how many seconds in order to achieve the desired time?

Homework Equations



V=change in distance/change intime
avg acceleration=change in velocity/time elapsed


The Attempt at a Solution



V before 25 minutes=5.4 m/s
V after 25 minutes=6.33 m/s
Avg. Acceleration=.24 seconds (know that's not right)
 
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  • #2
V before 25 minutes=5.4 m/s=Correct
Question is what is time taken
Acceleration given.

Now we call it u not V
You have intial velocity 5.4 m/s, distance to cover and use SUVAT to find time needed.
 
  • #3
The runner accelerates steadily at 0.22m/s over a time t seconds. Then he runs at that new speed for 300-t seconds.
 

Related to Acceleration of a runner to finish in his desired time

1. What factors affect a runner's acceleration?

Several factors can affect a runner's acceleration, including their physical fitness, technique, and the terrain they are running on. Other factors that can play a role include the runner's age, weight, and any existing injuries or health conditions.

2. How can a runner improve their acceleration?

To improve acceleration, a runner should focus on building strength and power through exercises such as plyometrics and weight training. They should also work on their running technique, including their stride length and arm movement. Consistent training and proper nutrition can also help improve a runner's acceleration.

3. What is the relationship between acceleration and speed?

Acceleration and speed are closely related, as acceleration is the rate at which an object's speed increases. Therefore, a faster acceleration will result in a higher speed. However, once a runner reaches their desired speed, their acceleration will decrease until they reach a constant speed.

4. How does air resistance affect a runner's acceleration?

Air resistance can have a significant impact on a runner's acceleration. As a runner moves through the air, they must push against it, which slows down their acceleration. This effect becomes more significant as the runner's speed increases, making it more difficult to maintain a high rate of acceleration.

5. Can a runner's acceleration change during a race?

Yes, a runner's acceleration can change during a race. Factors such as fatigue, changes in terrain, and environmental conditions can all affect a runner's acceleration. Additionally, a runner may strategically choose to conserve their energy at certain points in the race, resulting in a change in their acceleration.

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