(a)The world record for the 100-meter dash is 9.58 seconds (Bolt, 2009). Use the speed from part (a)
as his maximum velocity. Assume a sprinter accelerates at a constant rate up to their maximum
velocity, which is maintained for the remainder of the race, no matter how long it is. What is the
duration of the acceleration period at the beginning of the race?
(B)Also Determine the initial average acceleration in part(a)
average speed=100/9.58=10.43 m/s
that is the max velocity for the sprinter.
now the question is asking accleration up to a constant rattte NO MATTER how long it is.
Vf^2=Vi^2+2ad
10.43^2=0 + 2 a 100
a= you do it. This acceleration is for the entire 100m run. The question is flawed in this, as there can be any initial acceleration greater than this to reach max velocity. Lousy ill-conceived question.
in your problem statement, the sprinter could achieve his max velocity in a fraction of a second or it could take to the finish line
To determine the duration of the acceleration period at the beginning of the race, we need to determine the time it takes for the sprinter to reach their maximum velocity.
Given:
World record time: 9.58 seconds
Maximum velocity: Maximum velocity is reached at the end of the acceleration period
Step 1: Calculate the acceleration period duration
To calculate the duration of the acceleration period, we need to find the time it takes for the sprinter to reach their maximum velocity.
Using the equation of motion: v = u + at
Initial velocity (u) = 0 (since the sprinter starts from rest)
Final velocity (v) = maximum velocity reached by the sprinter
Since the acceleration is constant during the acceleration phase, the equation simplifies to: v = u + at
We can rearrange the equation to find the time (t):
t = (v - u) / a
Since the initial velocity (u) is 0, the equation becomes: t = v / a
Step 2: Calculate the initial average acceleration
To determine the initial average acceleration, we need to use the formula for average acceleration:
Average acceleration (a) = Change in velocity (v) / Time taken (t)
In this case, we can calculate the average acceleration during the acceleration phase.
Let's calculate:
a) Duration of the acceleration period:
Given:
Maximum velocity (v) = 9.58 m/s (World record time)
Acceleration (a) = [unknown]
t = v / a
9.58 / a = t
b) Initial average acceleration:
Given:
Time taken during the acceleration phase (t) = [result from step a]
Change in velocity (v) = maximum velocity (v)
Acceleration (a) = [unknown]
a = v / t
a = v / [result from step a]
Please provide the value of maximum velocity (v) in order to calculate the results in part (a) and part (b).
To determine the duration of the acceleration period at the beginning of the race, we need to calculate the time it takes for the sprinter to reach his maximum velocity.
(A) To find the duration of the acceleration period:
Step 1: Convert the maximum velocity from meters per second to meters per minute:
The world record for the 100-meter dash is 9.58 seconds, so the maximum velocity can be determined by dividing 100 meters by 9.58 seconds:
Maximum velocity = 100 meters / 9.58 seconds ≈ 10.44 meters per second
To convert this to meters per minute, we can multiply by 60 since there are 60 seconds in a minute:
Maximum velocity in meters per minute = 10.44 meters per second * 60 seconds ≈ 626.4 meters per minute
Step 2: Determine the distance covered during the acceleration period.
Since we know that the sprinter accelerates at a constant rate, we can use the kinematic equation:
v = u + at
Where:
v = final velocity (maximum velocity)
u = initial velocity (0 m/s, since the sprinter starts from rest)
a = acceleration
t = time
Since u = 0 m/s, the equation simplifies to:
v = at
We can rearrange this equation to solve for t:
t = v / a
Considering that the maximum velocity is 10.44 m/s and the sprinter starts from rest, the initial velocity is 0 m/s, so the equation becomes:
t = (10.44 m/s) / a
Step 3: Determine the acceleration.
The acceleration can be calculated using the formula:
a = (v - u) / t
Since the sprinter reaches his maximum velocity and starts from rest, and the time taken is the duration of the acceleration period (t), we can substitute these values into the equation:
a = (10.44 m/s - 0 m/s) / t
a = 10.44 m/s / t
Now we can use this equation to determine the initial average acceleration.
(B) To find the initial average acceleration:
Step 1: Substitute the maximum velocity into the equation:
a = 10.44 m/s / t
Step 2: Simplify the equation further to solve for t:
t = 10.44 m/s / a
Now you have the equation for the duration of the acceleration period (t) and the initial average acceleration (a). You can use the desired value for a to find the corresponding t, or vice versa.