Turner’s treadmill starts with a velocity of
−2.9 m/s and speeds up at regular intervals
during a half-hour workout.After 23 min, the
treadmill has a velocity of −7.9 m/s.
What is the average acceleration of the
treadmill during this period?
Answer in units of m/s2
(7.1m/s - 2.7m/s)/(33min X 60sec/min)
To find the average acceleration of the treadmill during this period, we can use the formula:
Average acceleration = (final velocity - initial velocity) / time
Given:
Initial velocity (u) = -2.9 m/s
Final velocity (v) = -7.9 m/s
Time (t) = 23 min = 23 * 60 seconds = 1380 seconds
Now, let's substitute the values into the formula:
Average acceleration = (-7.9 m/s - (-2.9 m/s)) / 1380 s
Simplifying:
Average acceleration = (-7.9 m/s + 2.9 m/s) / 1380 s
Average acceleration = -5 m/s / 1380 s
Average acceleration ≈ -0.0036 m/s^2
Therefore, the average acceleration of the treadmill during this period is approximately -0.0036 m/s^2.
To find the average acceleration of the treadmill during this period, we need to use the equation for average acceleration:
Average acceleration (a) = (change in velocity) / (change in time)
In this case, the change in velocity is the difference between the final velocity (-7.9 m/s) and the initial velocity (-2.9 m/s):
Change in velocity = (-7.9 m/s) - (-2.9 m/s) = -7.9 m/s + 2.9 m/s = -5 m/s
The change in time is the difference between the final time (30 minutes) and the initial time (23 minutes):
Change in time = 30 min - 23 min = 7 min = 7 * 60s = 420s
Now, we can calculate the average acceleration:
Average acceleration = (change in velocity) / (change in time)
= (-5 m/s) / (420s)
≈ -0.0119 m/s²
Therefore, the average acceleration of the treadmill during this period is approximately -0.0119 m/s².