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Physics 20: Kinematics

eMath Activity

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Use the provided data and instructions to perform the eMATH activity.

Vertical Projectile Motion

Purpose:

1. To plot a position-time graph from a set of position-time data values.

2. To create a velocity-time table of values from the position-time graph.

3. To plot a velocity-time graph of this motion.

Background:

An object that is thrown vertically into the air begins to decelerate as soon as it leaves the hand.  The initial velocity that the object possesses begins to diminish until it comes to a momentary stop.  It is at this moment that it reaches its greatest vertical displacement, and then it begins to fall back down to the same point where it was released.

This vertical projectile motion of the object can be graphed with both position-time and velocity-time graphs.  The shapes of each graph reveal a lot about the motion of the object.

Instructions:

1. Open the accompanying Excel spreadsheet and use the position-time table given to create a position-time graph using a suitable graphing program or a graphing calculator.

Make sure that you use an appropriate vertical scale to accommodate the large displacement values. (The graph should resemble a parabola.)
2. Using the position-time graph, determine the instantaneous velocity of the object at the times indicated in the table below.

Use the slopes of the tangent line method that you learned in Chapter 1 (or the method shown in the Chapter 1 eMATH) to do this.
3. Using the table of values that you just created, plot a velocity-time graph using a suitable graphing program or a graphing calculator.  Be sure to create a graph that has a vertical axis that extends into negative values so all the data can be plotted.

Analysis:

1. Is the velocity-time graph a straight line?
2. At what time does the velocity-time graph intercept the x-axis?  Look at the position-time graph.  What is the position of the object at this time?  Summarize this relationship in a sentence or two.
3. What are the displacements of the object at the 1 s and 7 s mark?
4. How do the velocities of the object compare at these two times?
5. How do the displacements and velocities compare at the 3 s and 5 s mark?
6. What general conclusion can you make about the velocity of the object as it goes up compared with when it comes down at the same heights?
7. Determine the slope of the velocity-time graph to find the acceleration of the object.
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