# Activity: Graphs of motion

#### Aims

- Understand the relationship between the graphs of motion and the motion itself.
- Interpret s-t, v-t and a-t graphs.
- Plot graphs or different examples.
- Understand the significance of gradient and area under graphs.

#### Simulations

There are many different simulations that can be used to plot graphs for different examples of motion, these are great for aiding understanding but at the end of the day you must be able to do it without the computer. So it is important that when asked to sketch a graph you actually sketch it before using the simulation to give the answer. In this activity you will use the moving man simulation from the University of Colorado PhET team, then you are going to build your own with GeoGebra

#### The moving man

Open the simulation below and play with the controls under the "charts" tab.

Sketch s-t, v-t and a-t graphs for the following situations then use the simulation to see if you were right. It is more fun to do this with a partner. (s_{o} is the starting displacement)

The simulation above may not work on all computers so you can use this one

s_{o }= -10 mu = 6 ms ^{-1}a = 0 ms ^{-2} | s_{o} = 0 mu = 0 ms ^{-1}a = 6 ms ^{-2} | s_{o} = -10 mu = 6 ms ^{-1}a = -6 ms ^{-2} |

For the last example tick the "show vectors" options for velocity and acceleration. Observe how these change (or not) during the motion.

#### Gradients

The gradient or slope of a line is defined as change in y/change in x. This can be written Δy/Δx. for an s-t graph this would be Δs/Δt which is the velocity.

- Use the simulation to check that higher velocity results in a steeper s-t graph.
- Estimate the velocity for the graph following graph

- Describe the motion in the next graph. Try to replicate it with the simulation.

Note that the gradient of a tangent to the line would be the instantaneous velocity.

The gradient of a v-t graph can be expressed as Δv/Δt this is the same as acceleration

- Estimate the acceleration for the graph below.

#### Area under the line

If we consider a graph of velocity vs time when velocity is a constant 2ms^{-1}

- Calculate the displacement of the body in 4s
- Calculate the area under the graph from 0s - 4s.

And for a body with constant acceleration.

- Use the suvat equation s = (u+v)t/2 to find the displacement
- Find the area under the line.

Another constant acceleration graph

- Without calculation deduce the displacement from 0 s to 4 s.

#### Motion in Algodoo

Algodoo is a very versatile programme that we will use a lot during this course. It is free and can be downloaded from here.

- Open a new scene in Algodoo.
- Use the circle tool to place a circle above the ground.
- Run the animation.
- Reset using the back button.
- Right click the circle and select material from the menu items. Change the material to rubber.
- Drop the ball again.

Stop playing with Algodoo for a minute and sketch the s-t, v-t and a-t graphs for the bouncing ball. When you've done that you can check your answers by drawing the graphs in Algodoo.

- Right click the circle.
- Choose "show plot".
- Select x axis "time" and y axis "y position".
- Run the simulation and observe the graph.
- Reset and repeat for velocity and acceleration.

If you want to make a cart here are some more detailed instructions Motion of a cart (Algodoo)

#### Motion in GeoGebra

Phet and Algodoo are great but you can't see the equations that are modeling the motion, if you really want to understand what's going on try building your own simulation with GeoGebra.

If you like fast cars how about this one:

And when you've done that