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course phy 201
An automobile traveling a straight line is at point A at clock time t = 4 sec, where it is traveling at 10 m/s, to point B at clock time t = 11 sec, where it is traveling at 20.5 m/s. Point A is 75 meters from the starting point and point B is 115 meters from the starting point. What are the average velocity and the average acceleration of the automobile during the specified time? What evidence is there that the acceleration is or is not uniform?Vave=(115-75m)/(11-4sec)=(40/7)=5.7m/s
Aave=(20.5m/s-10m/s)/(11-4)=(10.5/7)=1.5m/s2
The acceleration is not uniform because the first block has an acceleration of 2.5m/s/s and the second block has an acceleration of 1.86m/s/s.
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Good, but note that you only have information for one time interval. You don't know what the position or velocity is at t = 0, and you can't assume that either or both are zero at that instant.
They key is that if acceleration is uniform, the v vs. t graph is a straight line, so that the average velocity on any interval is the average of the initial and final velociites on that interval.
The average velocity is 5.7 m/s, as you have correctly concluded.
The average of the initial and final velocities, however, is over 15 m/s. Clearly not equal to the average velocity.
The conclusion is that the acceleration is not constant. In this case, in fact, it's far from constant.
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