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.
10 = (1/2) a t^2
20 = a (4)
a = 5 m/s^2
Thankyou, but I need to establish where within the run max acceleration occurs (what metre mark?)
I suspect if they turn around at the end, the max acceleration occurs there.
I think I know what you were looking for. 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 runner establishes max acceleration at the 2.5m mark in the race.
Hope I helped in time.
To determine where the maximum acceleration occurs during the shuttle run, we need to analyze the athlete's velocity and position during the sprint.
Acceleration, denoted as "a," is the rate of change of velocity. Since velocity is a vector quantity (meaning it has both magnitude and direction), acceleration can change in magnitude, direction, or both.
In this scenario, the athlete is sprinting out to 10m from the starting position, and it's mentioned that it takes 2 seconds. Let's break down the athlete's motion:
1. At the starting position (t = 0s): The athlete begins at rest and accelerates to reach their top speed while covering the initial distance of 10m. During this time, the acceleration is positive (in the same direction as the motion).
2. During the sprint (0s < t < 2s): The athlete continues sprinting at a constant velocity after reaching their top speed. Since velocity remains constant, acceleration is zero during this interval.
3. At the end of the sprint (t = 2s): The athlete completes the sprint and stops. At this point, their velocity decreases to zero, as they decelerate to come to a stop. The acceleration is negative (opposite direction to the motion) during this phase.
From the analysis above, we can conclude that the maximum acceleration occurs at the beginning (t = 0s) when the athlete is starting from rest and accelerating to reach their top speed. This is when the athlete is covering the initial 10m distance.
Justification: As the athlete accelerates from rest, the acceleration increases until they reach their top speed (covering the initial 10m). After reaching the top speed, acceleration decreases to zero. Hence, the maximum acceleration occurs at the start of the sprint.
Keep in mind that this explanation assumes a simplified scenario, considering constant acceleration during the initial run-up. In reality, factors like air resistance, varying terrain, and fatigue might affect the acceleration profile.