An athlete is training and is required to perform shuttle runs. From the starting position they sprint out to 10m (this takes 2 seconds). I know that a = 5m/s/s but I need to know at what metre within the run would maximum acceleration occur. Appreciate your help.

Question

An athlete is training and is required to perform shuttle runs. From the starting position they sprint out to 10m (this takes 2 seconds). I know that a = 5m/s/s but I need to know at what metre within the run would maximum acceleration occur. Appreciate your help.

thanks

Answer 1

for all we know the acceleration is constant. I actually suspect the force is greatest when pushing off the starting block and therefore acceleration is greatest at the start (F = m a), but there is nothing in your statement to help us with a versus t. Therefore assume a is constant.

d = (1/2) a t^2
10 = (1/2) a (2^2)
20 = 4 a
a = 5 m/s^2 indeed

Answer 2

I think I know what you are looking for, so starting off where Damon left off:

Max acceleration occurs when the velocity=acceleration.

Vi=0m/s^2
Vf=5m/s and
a=5m/s^2
d=?

Solve for d.

Vf^2=Vi^2+2ad

(5m/s)^2=0+2(5m/s^2)d

25=10d
25/10=d

d=2.5m

The sprinters will not keep accelerating indefinitely, so I think this what your teacher/professor had in mind. But a better question would be when will the velocity equal the acceleration.

Best

BTW, I answered this in your earlier post.

Answer 3

To determine at what meter within the run the maximum acceleration occurs, we'll need to calculate the distance covered during the 2-second sprint.

We can use the equation of motion:

d = ut + (1/2)at^2

where:
d is the distance covered,
u is the initial velocity,
a is the acceleration, and
t is the time taken.

Given that the athlete starts from rest, the initial velocity (u) is 0 m/s. The acceleration (a) is given as 5 m/s², and the time (t) is 2 seconds. Plugging in these values, we can find the distance (d).

d = 0 * 2 + (1/2) * 5 * (2^2)
= 0 + (1/2) * 5 * 4
= 0 + 2 * 5
= 0 + 10
= 10 meters

Therefore, the athlete would reach the 10-meter mark at the end of the sprint.

Since the athlete is required to perform shuttle runs, they sprint out to 10 meters and then would turn and sprint back. So, the maximum acceleration would occur at the turning point, which is halfway through the sprint out.

Hence, the maximum acceleration would occur at the 5-meter mark within the run.