course phy121
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.vI = 10m/s
vF = 20.5m/s
tI = 8sec
tF = 15sec
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.
vAve = (vI + vF) / 2 = (10m/s + 20.5m/s) / 2 = 15.25m/s
Average velocity is the average rate of change of position with respect to clock time, `ds / `dt, not (vI + vf) / 2.
If acceleration happens to be uniform then the v vs. t graph is a straight line, the average velocity occurs at the midpoint, and it will be true that vAve = (vI + vF) / 2. However unless it is known that acceleration is constant, this is not necessarily valid.
What therefore is the average velocity, and what is your conclusion about the uniformity of acceleration?
aAve = `dv / `dt = (vF - vI) / (tF - tI) = (20.5 - 10) / (15 - 8) = 1.5m/s/s
`ds = aAve * `dt = 15.25m/s * 7 = 106.75m
132m - 93m = 39m
since 39m is not equal to 106.75m, I would say that the acceleration was not linear.
This is a valid comparison, and if phrased right could be used to justify your correct conclusion.