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 m/s. what is the average acceleration of the treadmill during this period? answer in units of m/s squared
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To find the average acceleration of the treadmill, we need to use the formula for acceleration:
Acceleration (a) = (Change in velocity) / (Time taken)
In this case, we are given the initial velocity (u = -3.4 m/s) and the final velocity (v = -7.6 m/s). We also know that the time taken (t) is 26 minutes, or 26/60 = 0.433333 hours.
Now, let's calculate the change in velocity:
Change in velocity (Δv) = v - u
= (-7.6 m/s) - (-3.4 m/s)
= -7.6 m/s + 3.4 m/s
= -4.2 m/s
Next, we'll need to convert the time taken to hours:
t = 0.433333 hours
Now we can calculate the average acceleration:
Acceleration (a) = Δv / t
= (-4.2 m/s) / (0.433333 hours)
Since the question asks for the answer in units of m/s squared, we'll need to convert hours to seconds by multiplying by 3600 (since there are 3600 seconds in an hour):
Acceleration (a) = (-4.2 m/s) / (0.433333 hours) * 3600 s/hr
≈ (-4.2 m/s) / (0.433333 hours) * 3600 s/hr
≈ (-4.2 m/s) / (0.433333 * 3600) m/s^2
Now we can calculate the approximate value:
Acceleration (a) ≈ (-4.2 m/s) / (0.433333 * 3600) m/s^2
Simplifying this expression will give us the final answer for the average acceleration of the treadmill during this period in units of m/s^2.