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Constant Acceleration

Let’s just start with some definitions. (in 1 dimension)

Average velocity: v_\text{avg} = \frac{\Delta x}{\Delta t}

Average velocity: v_\text{avg} = \frac{v_1+v_2}{2}

Acceleration: a = \frac{\Delta v}{\Delta t}

  1. Card sort.
  2. Get a car and a track.  Set the track to some angle (something small – it doesn’t matter the actual angle).
  3. Let the car roll down the track and pass through a photo gate at some location. Measure the location of the photo gate, the time it takes to get to the photo gate and use the time from the photo gate to get the car’s speed.
  4. Repeat this for other positions.  Use it to fill out the following table.

Tentative Schedule - Google Sheets 2018-08-08 12-18-01.png

Yes, you will have to calculate the velocity.  Use this to make a graph of velocity vs. time.  It should be a straight line and the slope should be the acceleration.

Now use the position-time data to plot position vs. time squared.  The slope of this line should be 1/2 acceleration.

6. See if you can make a numerical model that agrees with your actual data.

7. Supposed I have two tracks with balls that can roll down towards each other.  How far up the track should ball 1 be so that they collide at the bottom?

summer_notes2_12-key-1.jpg

8. What if you push a car up a track?  How fast should it move so that it goes exactly 1 meter?

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