Motion Graphs

What Is Motion? Motion is when an object changes place or position. To properly describe motion, you need to use the following: Start and end position? Movement relative to what? How far did it go? In what direction did it go?

Motion & Graphs Motion graphs are an important tool used to show the relationships between position (distance), speed (velocity), and time. It’s an easy way to see how speed or position changes over time These types of graphs are called kinematic graphs. There are two types: Position (Distance) vs. Time graphs Speed (Velocity) vs. Time Graphs

Position Vs. Time Used to show an object’s position at a given time. Position: on y-axis Time: on x-axis

You Try It: Graphing Position Vs. Time Suppose you are helping a friend who is training for a track meet. She wants to know if she is running at constant speed. You mark the track in 50-meter increments and measure her time at each position during a practice run. Create a position-time graph using her data. Time (s) Position (m) 10 50 20 100 30 150

You Try It: Graphing Position Vs. Time When you’ve plotted all 4 points, you should get a graph that looks like this… What would her speed be? Choose any point, & divide distance (position) over time Time (s) Position (m) 10 50 20 100 30 150

You Try It: Graphing Position Vs. Time What would her speed be? 50m/10s = 5 m/s 100m/20s = 5 m/s Notice that this is a straight line - why?? She is moving at a constant speed - neither slowing down nor accelerating

You Try It: Graphing Position Vs. Time #2 Graph the motion of this car. Graph the points: (0,0), (1, 10), (2, 20), (3, 30), (4, 40), (5, 50). Your graph should look like this… What is this car’s velocity? A constant 10 m/s

What does slope have to do with it? Slope is the ratio of the rise (y-axis) to the run (x-axis) of a line on a graph. A bigger slope means a steeper line which means a faster speed.

Steeper Line = Faster Speed

Steeper Line = Faster Speed

Negative Slopes What does this graph mean??? And this one? They show an object that is slowing down - or decelerating. The first graph is slowly decelerating, while the second graph is quickly decelerating.

Basically… You might want to draw this graph in your Notebook

This is another really good graph to draw in your Notebook

Speed (s) = Distance (d) What Is Speed? Speed is the distance an object travels in a certain amount of time. To calculate speed, you use the following formula: Speed (s) = Distance (d) Time (t)

Graphing Speed Speed is usually graphed using a line graph, and it depicts the distance and time. Time is the independent variable, and thus is ALWAYS on the x-axis. Distance is the dependent variable, and is ALWAYS on the y-axis.

Velocity Velocity is the speed of an object, but the direction is also included. It is calculated the same as speed, but you must include a direction in your answer. Example: the bass boat was moving 12 mph toward the north.

Position Vs. Time - Changing Velocity Now consider a car that has a changing velocity. It is not moving at a constant rate, but getting faster by the second. What would this graph look like? You try it first…

Does your graph look like this? Be sure you have this one drawn

Predict: What does THIS GRAPH show?

This graph is for a car moving with a constant velocity of +5 m/s for 5 seconds, stopping abruptly, and then remaining at rest for 5 seconds. The straight line means its position is NOT changing.

Speed Vs. Time Used to show an object’s speed at a given time. Speed: on y-axis Time: on x-axis

Speed Vs. Time - Constant Speed This graph shows the speed versus time for a ball rolling at constant speed on a level floor. On a speed vs. time graph, constant speed is shown with a straight horizontal line. If you look at the speed on the y-axis, you see that the ball is moving at 1 m/s for the entire 10 seconds.

Speed Vs. Time - Constant Speed Compare this speed-time graph to the position-time graph for the ball. Both of the graphs show the exact same motion, even though they look different. If you calculate the slope of the lower graph, you will find that it is still 1 m/s.

You Try It: Graphing Speed Position Vs. Time Maria walks at a constant speed of 6 m/s for 5 seconds. Then, she runs at a constant speed of 10 m/s for 5 seconds. Create a speed-time graph using her data.

Speed Vs. Time - Changing Speed As we know, most objects don’t move at a constant speed. If a speed vs. time graph slopes up, then the speed is increasing. If it slopes down, then the speed is decreasing. If the graph is horizontal, then the object is moving at a constant speed. YOU MAY WANT TO DRAW THESE GRAPHS TOO!

Acceleration Acceleration is the rate of change of velocity. A change in velocity can be either a change in speed, or direction, or both. Deceleration is when acceleration has a negative value.

Acceleration The formula for calculating acceleration is: Acceleration (a) = final velocity (vf) – initial velocity (vi) time (sec) The unit for velocity, in this case, is m/s/s OR m/s2

Acceleration Math Problem A jet starts at rest at the end of a runway and reaches a speed of 80 m/s in 20 s. What is its acceleration? Acceleration (a) = final velocity (vf) – initial velocity (vi) time (sec) a = 80 m/s – 0 m/s = 4 m/s2 20 sec

Putting it All Together Which runner won the race? Albert won the race. He reached 100 meters first. Which runner stopped for a rest? Charlie stopped for a rest at 50m. How long did he stop for? Charlie stopped for 5 seconds. (13-8)

Putting it All Together 4. How long did Bob take to complete the race? Bob finished the race in 14 seconds 5. Calculate Albert's average speed. Speed = distance/time Speed = 100m/12s = Albert’s Speed = 8.3 m/s

Speed/Velocity/Acceleration Speed=Distance/Time Time=Distance/Speed Distance=Time X Velocity Time= Distance/Velocity Velocity=Distance/Time Velocity=Time X Acceleration Time= Velocity/Acceleration Acceleration=Velocity/Time