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Comparing positon (f), velocity (f '), & acceleration (f '')

1. Click the "reset time" & "Throw Ball" buttons to see the motion that produces the graph. Drag the point labeled “time” to trace the graphs. Move to the right to see what would have actually happened to the ball. If you move to the left you are in "rewind" mode going back in time.

2. Click the hide/show buttons to get the graphs you want. Click the X in the lower right to clear the traces that appeared on the graphs.

3. Hide f & f '', click "reset time", and click the red x. Drag time to the left untill the ball is at the top. What is unique about the velocity curve at this time? What would be unique about the position curve at this time (click show f ' to check your answer)? Would the acceleration be positive or negative (click show f '' to check)

4. Hide f & f '', click "reset time", and click the red x. Drag the "set A", "set B", & "set C" dots to adjust the velocity function (V = Ax^2 + Bx + C). Can you make the velocity a line? Concave up? Try to predict what the flight of the ball will look like. Then throw the ball to check your guess. If your velocity graph is too big, you can drag the "zoom" button to make it fit

5. Click hide f & hide f '' & hide c.p./i.p., click "reset time", and click the red x. Adjust the velocity as before & see if you can identify the critical values and inflection points. (click on show ip/cv) to check your answer.

6. Reload the web page and show all graphs. Trace to points where position is concave up. What do you notice about velocity & acceleration? Trace to points where velocity is positve. What, if anything, do you notice about position and acceleration? Adjust the graphs (drag "A", "B",& "C") & repeat.