Graphs of Linear Motion
Graphs of Linear Motion
Graphs of Linear Motion
Graphs of distance (position) versus time are commonly used to represent the linear motion of an object.
o X-axis (independent variable) – time
o Y-axis (dependent variable) – distance, position, displacement
o Slope – speed (velocity)
You try: To begin, consider a car moving with a constant, rightward (+) velocity of 25 m/s.
[pic]
|[pic] |Sketch the graphs of motion indicated for the car |[pic] |
| |shown above. | |
1. Calculate the slope of the position-time graph. What is its physical significance?
[pic]
2. Calculate the area beneath the velocity-time graph. What is its physical significance?
[pic]
Using the graph to the left, determine which runner is moving with the greatest speed. Explain.
Runner A, because it has the steepest
slope.
Consider a car moving with a constant velocity of +5 m/s for 5 seconds, stopping abruptly, remaining at rest (v = 0 m/s) for 5 seconds and then returning back to its original position.
[pic]
Now, sketch a position time graph representing the velocity of the car.
[pic] [pic]
Graphs of Changing Velocity
Now consider a car moving with a changing, rightward (+) velocity – that is, a car that is moving rightward and speeding up or accelerating.
[pic]
Sketch a position-time graph for the cars above.
[pic]
Sketch the graphs below accordingly.
|[pic] |[pic] |[pic] |
|Time |Time |Time |
|Constant speed in positive direction |Constant speed in negative direction |Standing still |
Graphs of Accelerated Linear Motion
Consider a car with a rightward (+) changing velocity. That is, a car moving to the right and speeding up or accelerating. Since the car is moving in the positive direction and speeding up, it is said to have a positive acceleration.
[pic]
|Time (s) |0 - 1 |1 - 2 |2 - 3 |3 - 4 |4 - 5 |
|Distance (m) |2 |6 |10 |14 |18 |
|Velocity (m/s) |4 |8 |12 |16 |20 |
|Acceleration |4 m/s2 (speed increased 4 m/s each second) |
Sketch a velocity-time graph for the cars above.
|[pic] | |
| |What does the slope of the graph represent? |
| | |
| |acceleration |
| | |
| |Calculate the area underneath the slope. What is its physical significance? |
| |distance, [pic] |
Characteristics of Velocity vs. Time graphs
o X-axis (independent variable) – Time
o Y-axis (dependent variable) – Velocity
o Slope - Acceleration
• If slope is zero, than acceleration is _______zero_________.
• If slope is positive, than acceleration is _______positive_____.
• If slope is negative, than acceleration is _______negative_____.
How can you tell if the object is moving in the positive direction (i.e., positive velocity) or in the negative direction (i.e., negative velocity)?
Positive Velocity Negative Velocity
[pic] [pic][pic][pic]
How can you tell if the object is speeding up or slowing down?
Speeding Up Slowing Down
[pic] [pic]
Sketch the graphs below accordingly.
|[pic] |[pic] |[pic] |
|Time |Time |Time |
|Increasing speed |Decreasing speed |Constant speed, then decreasing speed to stop. |
Consider the graph below. The object whose motion is represented by this graph is ... (circle all that apply):
a. moving in the positive direction.
b. moving with a constant velocity.
c. moving with a negative velocity.
d. slowing down.
e. changing directions.
f. speeding up.
g. moving with a positive acceleration.
h. moving with a constant acceleration.
-----------------------
How can you tell that the car is moving at a constant speed?
[pic]
The slope is the velocity.
The area is the distance traveled.
Time (s)
Distance (m)
To linearize graph, plot (time)2 on the x-axis.
Position
Position
Position
Equations needed to solve for velocity will be learned at a later date.
Velocity values are for the end of the time interval.
backwards
forewards
+ away
- towards
Position
Position
+ away
- towards
Position
How can you tell that the car is speeding up?
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