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course Phy 231
2-5-11 about 12:00am
A bee is making a beeline for its hive. Its velocity is measured at a distance of 75 meters from the observer and again at distance 145 meters from the observer. The clock times at these two positions are t = 9 sec and t = 16 sec, and the measured velocities are 3 m/sec and 13.5 m/sec. What is its average velocity during this time? What is its average acceleration during this time? Is it possible that the acceleration is uniform?
vAve= (3m/sec + 13.5m/sec)/2= 8.25m/sec
aAve= (13.5m/sec – 3m/sec)/(16sec – 9sec)= 1.5m/sec/sec
If no variables, such as wind, were taken into account then acceleration could be uniform.
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Somebody probably does know, but neither you nor I know how a real bee's velocity tends to change as it approaches its hive. Certainly the circumstances will affect it, but there is no reason to assume that the basic nature of the acceleration would be unform.
However we do know that if acceleration is uniform, then v is a linear function of t. And by the definition of the average value of a function the average velocity on an interval is the integral of the velocity function on that interval, divided by the duration of the interval. From this (or from consideration of the linear v vs. t graph) we conclude that if acceleration is uniform, the average velocity is the mean of the initial and final velocities.
This might be helpful in answering that last question.
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