course phy 121
4/21 3:30
An airplane on a runway has velocity 10 m/s at clock time t = 8 sec and velocity 20.5 m/s at clock time t = 15 m/s. Find its average velocity and its average acceleration during this time interval, and determine whether the acceleration might be uniform, if the distances from a certain roadkill on the runway are 93 meters and 132 meters at the
respective clock times.
At t = 8 s the velocity is 10 m/s, and at t = 15 s the velocity is 20.5 m/s. So its average velocity over this period is (10 m/s + 20.5 m/s) / 2 = 15.25 m/s. Its avg. acceleration would be (10 m/s + 20.5 m/s) / 7 s, where 7 s is the interval, 30.5 / 7 = 4.36 m/s/s.
change in velocity is 10.5 m/s, average acceleration is 1.5 m/s^2; I believe you'll immediately see your error but let me know if not
Given the distances from the roadkill it does not appear to be uniform acceleration, as you can find average velocity with the distance something has moved divided by the time interval. The distance would be 132 - 93 = 39 m, so over the 7 second interval the plane moved 39 meters, when you divide 39 / 7 = 5.57 m/s.
This is the correct average velocity.
Your previous result 15.25 m/s is the average of initial and final velocities, and is not necessarily equal to average velocity.
If acceleration is uniform then the average of initial and final velocities will be identical to the average velocity (be sure you understand how the linearity of the v vs. t graph ensures this; ask if you're not sure).