Turner’s treadmill starts with a velocity of −1.9 m/s and speeds up at regular intervals during a half-hour workout.After 36 min, the treadmill has a velocity of −7.6 m/s.
What is the average acceleration of the treadmill during this period?
Answer in units of m/s2
The average acceleration of the treadmill during this period is -0.2 m/s2.
To find the average acceleration, we need to use the formula:
Average acceleration = (change in velocity) / (change in time)
Given that the initial velocity is -1.9 m/s and the final velocity is -7.6 m/s, we can calculate the change in velocity:
Change in velocity = final velocity - initial velocity
= -7.6 m/s - (-1.9 m/s)
= -7.6 m/s + 1.9 m/s
= -5.7 m/s
Next, we need to calculate the change in time. The workout duration is given as 36 minutes, which can be converted to seconds:
Change in time = workout duration
= 36 min
= 36 min * 60 s/min
= 2160 s
Now we can calculate the average acceleration:
Average acceleration = (change in velocity) / (change in time)
= (-5.7 m/s) / (2160 s)
≈ -0.00264 m/s^2
Therefore, the average acceleration of the treadmill during this period is approximately -0.00264 m/s^2.
To find the average acceleration of the treadmill, we can use the formula:
average acceleration = (final velocity - initial velocity) / time
Here, the initial velocity is -1.9 m/s, the final velocity is -7.6 m/s, and the time is 36 minutes.
First, let's convert the time from minutes to seconds. Since there are 60 seconds in a minute, 36 minutes is equal to 36 x 60 = 2160 seconds.
Now, we can substitute these values into the formula:
average acceleration = (-7.6 m/s - (-1.9 m/s)) / 2160 s
Simplifying this expression:
average acceleration = (-7.6 m/s + 1.9 m/s) / 2160 s
average acceleration = -5.7 m/s / 2160 s
average acceleration = -0.00264 m/s²
Therefore, the average acceleration of the treadmill during this period is approximately -0.00264 m/s².