Students will learn how to graph motion vs time. Specifically students will learn how to take the slope of a graph and relate that to the instantaneous velocity or acceleration for position or velocity graphs, respectively. Finally students will learn how to take the area of a velocity vs time graph in order to calculate the displacement.
For a graph of position vs. time. The slope is the rise over the run, where the rise is the displacement and the run is the time. thus,
Note: Slope of the tangent line for a particular point in time = the instantaneous velocity
For a graph of velocity vs. time. The slope is the rise over the run, where the rise is the change in velocity and the run is the time. thus,
Note: Slope of the tangent line for a particular point in time = the instantaneous acceleration
- One must first read a graph correctly. For example on a position vs. time graph (thus the position is graphed on the y-axis and the time on the x-axis) for a given a data point, go straight down from it to get the time and straight across to get the position.
- If there is constant acceleration the graph vs. produces a parabola. The slope of the vs. graph equals the instantaneous velocity. The slope of a vs. graph equals the acceleration.
- The slope of the graph vs. can be used to find acceleration; the area of the graph vs. can be used to find displacement. Welcome to calculus!
What is a Graph
Watch this Explanation
Time for Practice
- The position graph below is of the movement of a fast turtle who can turn on a dime. a. Sketch the velocity vs. time graph of the turtle below. b. Explain what the turtle is doing (including both speed and direction) from: i) 0-2s. ii) 2-3s. iii) 3-4s. c. How much distance has the turtle covered after 4s? d. What is the turtle’s displacement after 4s?
- Draw the position vs. time graph that corresponds to the velocity vs. time graph below. You may assume a starting position . Label the axis with appropriate values.
- The following velocity-time graph represents 10 seconds of actress Halle Berry’s drive to work (it’s a rough morning).
a. Fill in the tables below – remember that displacement and position are not the same thing!
|Instantaneous Time (s)||Position (m)|
|Interval (s)||Displacement (m)||Acceleration||0 sec||0 m|
b. On the axes below, draw an acceleration-time graph for the car trip. Include numbers on your acceleration axis.
c. On the axes below, draw a position-time graph for the car trip. Include numbers on your position axis. Be sure to note that some sections of this graph are linear and some curve – why?
- Two cars are drag racing down El Camino. At time , the yellow Maserati starts from rest and accelerates at . As it starts to move it’s passed by a ’63 Chevy Nova (cherry red) traveling at a constant velocity of 30 m/s. a. On the axes below, show a line for each car representing its speed as a function of time. Label each line. b. At what time will the two cars have the same speed (use your graph)? c. On the axes below, draw a line (or curve) for each car representing its position as a function of time. Label each curve. d. At what time would the two cars meet (other than at the start)?
1c. 25 m
1d. -5 m
2. discuss in class
3. discuss in class
4b. 3 sec
4d. 6 sec