Graph Trends
Motion Maps
- Represent the position, velocity and acceleration of an object.
In the graph above, it's shown that object B is travelling at a faster rate than object A. You know this because object B travelled a further distance than A in the same given amount of time. When the arrows are longer, it implies that the object is moving faster.
Displacement
The displacement of an object is how far away the object ends up from its starting point. You are always measuring the distance between two points. The way to calculate this would be to observe the change (Δ) in position, which would be (x final - x initial).
Path Length
The path length of an object is the distance it has physically travelled. So, if it went 5 meters at 1 m/s in the northern direction, then travelled south for 7 meters at 1 m/s, the path length would be 12 m.
Speed
The speed is how fast the object is going on the path
Velocity
The velocity of an object is the change in position over the change in time.
Practice Problems!
Describe the motion of the object.
The object begins at the 20 meter mark on the y axis, maintaining a velocity of 0 m/s for the first second. It then travels 20 m/s for two seconds in a positive slope, until it plateaus again at 60 meters. It obtains a velocity of 0 m/s for a second and a half, before continuing on at a negative slope of about 26 m/s.
How much distance did the object travel?
It travelled a total of 80 meters. It began at the 20 meter position, proceeding to the 60 meter position, and eventually going back to the 20 meter position.
What was the total displacement?
The total displacement was 0, because it started and finished at the same point on the position axis.
Mathematical Equation describing motion
x = vt +x0 <-- (starting position)
Velocity Graphs
A velocity graph is represented with a straight line, no slopes are involved. The x axis usually relates to the time, and the y axis is the object's distance over time (velocity).
Determining area
Calculate the area up to 5 seconds in the graph above.
5 s * 10 m/s = 50 ms/s = 50 meters
This area represents the object's displacement, so the object ended up 50 meters from its starting point.
How does this relate to our world?
Objects in motion always have some form of velocity. Whether it be the car driving past your house, or the ball being thrown at baseball practice, all objects that are moving have velocity. Constant velocity is measured by the displacement over time. If you drove 60 mph for an hour, your constant velocity would be 60 miles per hour. Ideas like displacement also are seen in our everyday life. If you began a walk at your house, and travelled around the neighborhood to finish your walk at your house, your displacement would be 0. There was no change in the starting or finishing position in that situation. An object in motion also always has some type of speed. Whether it be going fast or slow, speed can be measured as distance over the amount of time.
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