Motion-Study 1D Kinematics B E Mays –S Caesar

1D Kinematics Motion Graphs

Motion & Graphs Motion graphs are an important tool used to show the relationships between position, speed, 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 vs. Time graphs Speed vs. Time Graphs

Graphing Motion

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

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 can do: 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

PLOT 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

Graphing Position Vs. Time Lab#2 Graph the points: (0,0), (1, 10), (2, 20), (3, 30), (4, 40), (5, 50). Draw a chart of positon and time for the above pictorial diagram What is the velocity of the car? Is it constant?

Position verses Time Graph the motion of the chart in the previous slide. Your graph should look like this… Your graph should look like this…

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 value of the slope means a steeper line which means a faster speed.

Steeper Line = Faster Speed Let us consider two different cars (red & blue) moving at different speed in the same direction. Going rightwards here is considered as apositive direction. Study the slopes of these cars Steeper Line = Faster Speed

Steeper Line = Faster Speed

Negative Slopes What does this graph mean??? What does the negative slope indicate? They show an object that is moving in opposite direction with constant speed . The first graph indicates that the car has smaller constant speed, while in the second graph the object has higher constant speed in negative direction. Comparing the slopes , the 2nd graph has steeper slope

Basically… You might want to study this graph in your next lessons which are velocity –time graphs. The slopes of v-t graphs indicate acceleration of an object.

This is another really good graph to draw in your lab book

. Distance, Velocity & Acceleration Now consider a car that has a changing velocity. It is not moving at a constant rate, but getting faster by the second. Please create a chart of position and time, for such a car. Also draw the pictorial diagram for the car moving this way.

Position Vs. Time - Changing Velocity What would this graph look like? You try it first…

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

Try It: GrAPHING Position Vs. Time #3 What would the graph look like for a car that traveled 10 m in the 1st second, 15 m by the 2nd second, 25 by the 3rd second, and 40 m by the 4th second?

Predict: What does THIS GRAPH indicate?

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 parallel to x- axis. Draw a pictorial diagram and create a chart for speed – time. Try plotting it on a speed –time graph.Study the plotted graph. 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. ( in class demo done)

Graphing Speed 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. Has an acceleration. If it slopes down ( steeper negative slope), then the car speeds up at constant rate in negative direction. It indicates that the car has higher constant acceleration. REMEMBER: The speed –time slope indicates acceleration. Its SI unit is meter/second square

Speed Vs. Time - Changing Speed It is decreasing at a constant rate, if the slope of speed-time graph is shallower. If the graph is horizontal, then the object is moving at a constant speed. YOU MAY WANT TO DRAW THESE GRAPHS TOO!

Summing it All Together Chech your understanding 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)

summing 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

Thank You