IMPETUS Roller Coaster Camp

Motion with Acceleration

1.Warm up Activities

  • Let’s start with a brief review of motion at a Constant Speed
  • Open up Excel and we’ll create a table of time and distance traveled
  • Then we’ll graph it

Notes:

Notes:

  • There are at least two different ways we can compute the distances
  • Both are based on

Remember in Excel, cell references are relative unless we change that.

How?

  • Use the F4 key to toggle through the options.
  • $ signs indicate pieces that will be kept fixed. That is their location will not change when you copy the formula to other cells.

Let’s look at the effect.

  • Note the $ signs in the $C$10 which means that when we copy the formula down the column it will always refer to that particular location. Watch!

  • Now graph it
  • Do you remember how?

Are all graphs straight lines?

What is the slope of the line? (Be careful about units here.)

Can we get an equation for the line?

2.Work Out

  1. Now look at the effect of acceleration on speed.
  • What is acceleration?
  • What are its units?
  • Repeat the warm-up except we will graph speed against time with a constant acceleration.
  • What about the initial speed?
  • What about the direction?
  • What does negative acceleration mean?
  • What happens to the graph?
  • We need to be careful about the direction of motion, not just its speed – this is called velocity.
  • For straight line motion simply using + and – is enough
  • Sometimes we need more information such as up-down, left-right, or North-South, East-West
  1. Now what happens to position when there is acceleration?
  • Think about a ball being thrown straight up in the air.
  • We’ll model this in Excel
  • To start we’ll create a spreadsheet similar to this:

How do we compute the speed column entries?

How does that effect the distance computation?

We need a step-by-step approach. (Technically this is called Euler’s Method.)

3.Stretch

  1. First let’s think about acceleration that changes
  • Why should acceleration change?
  • Air resistance typically depends on speed
  • What does terminal velocity mean?
  • How do we incorporate a changing velocity into our spreadsheet model?

  1. What about motion in two dimensions – like throwing a baseball or football?
  • Horizontal and vertical components
  • What are they? (We saw something of this in the Numb3rs activity.)
  • Do they react the same way to gravity?
  • What about other forces?