An athlete is training and is required to perform shuttle runs. From the starting position they sprint out to 10m (this takes 2 seconds).
Where would the maximum acceleration occur? Justify your answer.
Please help! Thankyou.
To determine where the maximum acceleration occurs during the athlete's shuttle runs, we need to understand the relationship between acceleration, velocity, and displacement.
Acceleration is the rate at which the athlete's velocity changes over time. In mathematical terms, acceleration (a) can be calculated as the change in velocity (∆v) divided by the change in time (∆t):
a = ∆v / ∆t
From the given information, we know that it takes the athlete 2 seconds to sprint out to 10 meters. Assuming a constant acceleration, we can calculate the average velocity (v) during this period:
v = ∆d / ∆t
where ∆d is the displacement, which in this case is 10 meters. Plugging in the values, we have:
v = 10m / 2s = 5m/s
Since we know the displacement and time, we can calculate the average acceleration (a) using the equation:
a = ∆v / ∆t
Here, ∆v will be the change in velocity, which is the final velocity (vf) minus the initial velocity (vi). Since the initial velocity is zero (starting from rest), the calculation becomes:
a = vf / ∆t
Substituting the known values:
a = 5m/s / 2s = 2.5m/s^2
So, the average acceleration over the entire 10m sprint is 2.5 m/s^2.
However, to determine where the maximum acceleration occurs, we need to consider the fact that the athlete is sprinting out to 10m and then presumably decelerating to stop at the end.
Since the athlete reaches a maximum speed of 5m/s at the end of the 10m sprint, the maximum acceleration will occur during the initial phase when the athlete is sprinting from a standstill to reach their maximum speed. Therefore, the maximum acceleration occurs at the beginning of the sprint.
In summary, the maximum acceleration occurs at the beginning of the shuttle run when the athlete sprints from the starting position to reach their maximum speed of 5m/s.