Acceleration of world-class sprinter

In summary, a typical world-class sprinter accelerates to his maximum speed in 4 seconds. If the same runner finishes a 100-meter race in 9.1 seconds, the average acceleration during the first 4 seconds can be found by solving for v2 and using the formula a = (v2-v1)/t1. This involves finding the distance traveled during the first 4 seconds and the distance traveled at a constant speed for the remaining 5.1 seconds, and setting them equal to the total distance of 100 meters.
  • #1
kring_c14
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Homework Statement



A typical world-class sprinter accelerates to his maximum speed in 4 s. If such a runner finishes a 100-m race in 9.1 s, what is the runner’s average acceleration during the first 4 s?

:cry:
thank you for your help...
 
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  • #2
A typical world-class sprinter accelerates to his maximum speed in 4 s. If such a runner finishes a 100-m race in 9.1 s, what is the runner’s average acceleration during the first 4 s?

this will be a two-part problem.

1) The first part is him accelerating from 0 to Vmax in 4 sec.

2) The second part will be him at steady speed, Vmax for 5.1 sec.

If you can express both of these parts algebraically (without numbers) as meters run, then you can add those together to equal the Total Distance Run and solve for that max velocity.

Having the max velocity, you can go back to the first part and find the acceleration.
 
  • #3
Divide the race into two parts i) where he accelerates at a constant rate 'a' for 4 sec, and the second part where he travels at the constant speed a*(4 sec). Write down an expression for how far he travels in i) and an expression for how far he travels in ii). The sum of those two expressions is 100m. Can you solve for a?
 
  • #4
i don't get it...sorry...
 
  • #5
His maximum speed is v which he reaches at 4s... his initial speed is 0. What distance does he travel over the first 4 seconds, in terms of v? Just plug into the appropriate equation.
 
  • #6
kring_c14 said:
i don't get it...sorry...

Here's the question right?

A typical world-class sprinter accelerates to his maximum speed in 4 s. If such a runner finishes a 100-m race in 9.1 s, what is the runner’s average acceleration during the first 4 s?

For the first part of his motion, he's accelerating from a velocity of 0 to a velocity of V (we don't know the number yet, but that's ok)€.

So we can find the distance run so far by:

1) x1 = 1/2(v1 + v2)t1, where v1 = 0, and t1 = 4s

For the second part, it's simply

2) x2 = v2t2, where we don't know v2 still, but we know t2 = 5.1s

Since the whole race is 100 meters long, and the equations above give us two distances during the time he raced, we can add those two distance, 1) and 2), together to equal the third distance, 100m:

3a) x1 + x2 = 100m

or

3b) 2s*v2 + 5.1s*v2 = 100m

you can solve 3b for v2 to get the velocity.

once you have v2, you can go back to 1) and use the equation:

4) a*t1 = 1/2(v1 + v2)

solving 4) for "a" gives you your acceleration.
 
  • #7
thank you so much!thank you!
 
  • #8
Pythagorean said:
4) a*t1 = 1/2(v1 + v2)

solving 4) for "a" gives you your acceleration.

You mean a = (v2-v1)/t1.
 

What factors contribute to the acceleration of a world-class sprinter?

A world-class sprinter's acceleration is influenced by a combination of physiological, biomechanical, and training factors. These include muscle strength and power, running technique, reaction time, and training regimen.

How does muscle fiber composition affect sprinting acceleration?

The proportion of fast-twitch muscle fibers in a sprinter's muscles plays a significant role in their acceleration. Fast-twitch fibers have a higher capacity for generating force and speed, making them essential for explosive movements like sprinting.

What role does technique play in sprinting acceleration?

Sprinting technique is crucial for maximizing acceleration. A sprinter must have proper body positioning, arm swing, and foot strike to generate maximum power and minimize energy loss. Small improvements in technique can lead to significant gains in acceleration.

Can a sprinter's acceleration be improved through training?

Yes, a world-class sprinter's acceleration can be improved through specific training techniques. This includes strength training to increase muscle power, plyometric exercises to improve explosive movements, and sprint-specific drills to refine technique and reaction time.

How does reaction time affect sprinting acceleration?

Reaction time, the time it takes for a sprinter to respond to the starting gun, is a critical factor in sprinting acceleration. A faster reaction time allows for a quicker start, giving the sprinter an advantage over their competitors. Reaction time can be improved through specific training drills and exercises.

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