The Moving Man
Purpose: Students will select the sign of the initial position, velocity, and acceleration to match graphs of the moving man’s motion. Students will attempt to discover the connections between graphs.
1)Go to Familiarize yourself with the program, then answer the following questions.
On each question 2 through 5, I would like you to try predicting the shape of the graph and then run the experiment and see if you were right:
2)What does constant velocity look like on a position vs. time graph?
3)What does constant velocity look like on a velocity vs. time graph?
4)What does constant acceleration look like on a position vs. time graph?
5)What does constant acceleration look like on a velocity vs. time graph?
6)Select initial values for position, velocity, and acceleration to matchboth of the following position vs. time and velocity vs. time graphs. When you match the curves indicate whether each variable’s initial condition was positive, negative, or zero.
- position: (-) (0) (+)
velocity: (-) (0) (+)
acceleration: (-) (0) (+) - position: (-) (0) (+)
velocity: (-) (0) (+)
acceleration: (-) (0) (+) - position: (-) (0) (+)
velocity: (-) (0) (+)
acceleration: (-) (0) (+) - position: (-) (0) (+)
velocity: (-) (0) (+)
acceleration: (-) (0) (+)
7)Describe the motion when initial velocity and acceleration have the same sign. Does it matter if both are positive or both are negative? Choose an initial position, also. Choose at least one case (v and a both positive or negative). By drawing the 3 small sketches to the left (i.e. the graphs or x(t), v(t), and a(t), predict the shapes of all three graphs in this simulation. Then run the simulation to see if you were right. Draw the graphs given by the simulation on the right hand side. You should have a total of 6 graphs, at least.
8)Describe the motion when initial velocity and acceleration have opposite signs. Does it matter which is positive and which is negative? Choose an initial position. Choose at least one case for v and a having different signs.By drawing the 3 small sketches to the left (i.e. the graphs or x(t), v(t), and a(t), predict the shapes of all three graphs in this simulation. Then run the simulation to see if you were right. Draw the graphs given by the simulation on the right hand side.
9)Create a few more cases (random) and look at the graphs of x(t) and v(t). Do you notice anything that may relate these two graphs? (hint: the easiest to see the connection between x(t) and v(t) is by choosing positive and negative values for v initial and run each case looking at v(t) and x(t) graphs). Write your conclusion below.It helps to keep a=0 first, but this is not a necessary condition to discover the connection wanted.
10)Do the a similar caseas for part 9) but this time pay close attention to v(t) and a(t). (hint: the easiest to see the connection between a(t) and v(t) is by choosing positive and negative values for a initial and run each case looking at v(t) and a(t) graphs). Can you see any connection between these two graphs? Explain.