turner's treadmill starts with a velocity of -3.4 m/s and speeds up at regular intervals during a half hour workout. after 26 minutes the treadmill has a velocity of -7.6
To find the acceleration of the treadmill, we can use the formula:
acceleration = change in velocity / time
In this case, the change in velocity is:
(-7.6 m/s) - (-3.4 m/s) = -7.6 m/s + 3.4 m/s = -4.2 m/s
The time interval is:
26 minutes = 26 * 60 seconds = 1560 seconds
So, the acceleration of the treadmill is:
acceleration = (-4.2 m/s) / (1560 s) = -0.00269 m/s²
To find the acceleration of Turner's treadmill, we can use the formula for average acceleration:
Acceleration (a) = (Change in Velocity)/(Change in Time)
Given that the initial velocity (u) is -3.4 m/s and the final velocity (v) after 26 minutes (26/60 = 0.433 hours) is -7.6 m/s, we can calculate the acceleration.
Change in Velocity = v - u = -7.6 m/s - (-3.4 m/s) = -7.6 m/s + 3.4 m/s = -4.2 m/s
Change in Time = 0.433 hours
Now, we can calculate the acceleration using the formula:
Acceleration (a) = (Change in Velocity)/(Change in Time) = -4.2 m/s / 0.433 hours
To convert hours to seconds, we can multiply by 60 (minutes) and 60 (seconds):
Acceleration (a) = -4.2 m/s / (0.433 hours * 60 minutes/hour * 60 seconds/minute)
Acceleration (a) ≈ -0.042 m/s^2
Therefore, the acceleration of Turner's treadmill during the first 26 minutes of the workout is approximately -0.042 m/s^2.