# ElizabethE:Acceleration

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## What should know about constant acceloration and the quantity of acceloration when they are done?

1) Acceloration is in the direction of the change in motion, not the direction of motion.

2) Acceloration is the rate of change of an object's velocity

3) Representations of acceloration (motion diagram, graphs)

4) Kinematic equations for constant acceloration.

## Describe how you help your students construct the ideas of motion with constant acceleration, and the physical quantity of acceleration.

1) Acceloration is in the direction of the change in motion, not the direction of motion.

Students will start with observational experiments with an object that is not moving at constant speed. Have the students draw motion diagrams. How are the lenghts of the arrows different from a constant velocity situation. Have the students drew in delta v arrows. We are looking for a way to describe the change in velicity. Mke sure that delta v is not always in the direction of motion.

2) Acceloration is the rate of change of an object's velocity

Next do an observational experiment with constant acceloration (This can be the same experiment as above.). Falling objects work well. A vidio may be used so students can take data or they may may be given the data. Ask the students to draw motion diagrams with delta v arrows. Have students plot v vs. clock reading. What is the meaning of the slope? (acceloration, the rate of change in velocity) Relate this to the motion diagram. (i.e. the ddelta v is related to acceloration) Have the students write a mathimatical relationship between v and clock reading ($v = at + v0$ or$a = (v-v0)/t$).

3) Representations of acceloration (motion diagram, graphs)/ Kinematic equations for constant acceloration

Now ask the students to plot position vs clock reading for the last experiment. How does this compare to the graph of constant velocity? Can we use the same equation to discribe the relationship between position and clock reading? Here the students will need to do a remon sum approximation of the integral. Argue that for small time internals the velocity can be approximated by Failed to parse (lexing error): v ≈ Vave = (v1+vo)/2

```so that $x = vt +x0$ becomes $x = (v1 +v0)t/2 + x0$ the first of nextons equations for constant acceloration. Ask students to take another look at the v vs. clock reading graphs. What is the area under the curve? Ask the students to write a mathematical equation. They will come out with the result that the area under the curve is $(v1+vo)/2$, but this was the estimated displacement. What was the area under the v vs. clock reading graph for constant velocity?
```

Now the students will finish the mathimatical derivation of a relationship between a and position. Ask the students to use the two equations they have constructed to find this relationship. $v = at + v0$ and $x = (v1 +v0)t/2 + x0$, so $x = (v1 +v0)t/2 + x0 =(at +vo+vo)t/2 + x0 =0.5a*t^2 + v0*t + x0$.

4) Testing Experiments:

Students can easily test this experiment, by pluging in the experimental values of a and v0 found graficaly and the initial postion x0. Does the graph of this equation match the experimental curve?

Another testing experiment that can be done is the “moving man experiment” at http://phnet.colorado.edu