course phy201
2/10/2010 6:05p.m
Seed 3.1 The problem:
A ball starts with velocity 0 and accelerates uniformly down a ramp of length 30 cm, covering the distance in 5 seconds.
What is its average velocity?
answer/question/discussion (start in the next line):
'ds=vave * 'dt
30cm = vave * 5s
6 cm/s is the average velocity
@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
#$&*
If the acceleration of the ball is uniform then its average velocity is equal to the average of its initial and final velocities.
You know its average velocity, and you know the initial velocity is zero.
What therefore must be the final velocity?
answer/question/discussion (start in the next line):
the final velcity is 6 cm/s * 2 = 12 cm^2/s^2
@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
#$&*
By how much did its velocity therefore change?
answer/question/discussion (start in the next line):
Its velocity doubled from the starting point at zero to the final position at 6 cm/s
@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
#$&*
At what average rate did its velocity change with respect to clock time?
answer/question/discussion (start in the next line):
average rate = change velocity / change clocktime
average rate =6cm/s / 5 seconds
average rate = 1.2 cm/s^2
The average velocity is used in calculating the final velocity.
However the average velocity is not used in calculating the change in velocity, which is based on the initial and final velocities.
@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
#$&*
What would a graph of its velocity vs. clock time look like? Give the best description you can.
answer/question/discussion (start in the next line):
A graph of Velocity vs clocktime would have velocity on the the vertical axis and clocktime on the horizontal axis
it would be a linear graph the slope would be a positive 1.2 cm/s.
In calculating the slope you should specify the two graph points you used, and the rise and run of the graph.
&#Please compare your solutions with the expanded discussion at the link
Solution
Self-critique your solutions, if this is necessary, according to the usual criteria. Insert any revisions, questions, etc. into a copy of this posted document. Mark any insertions with &&&& so they can be easily identified. &#