CAPM Unit Summary:
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In CAPM model, we learned that the curved lines
on the graph indicates acceleration. We also learned that the positive
direction indicates an object is moving forward and a negative direction
indicates an object in moving backwards.
Displacement:
The displacement is the distance the
object traveled from it’s starting point. The formula used to calculate the
displacement is x final - x initial.
Velocity
The velocity of an object is the change
in position over the change in time.
To calculate the velocity, use the formula: (change in position over change in time)
V= DeltaX
Delta T
The
instantaneous velocity can be found at any point by finding the average
velocity. The average velocity will be the same as the instantaneous
velocity at the mid time. If the graph has a constant velocity and
starting position you can predict the velocity at any point.
Reading a V vs T Graph:
In a velocity vs time graph anything above the X axis is the positive direction. If the line is going in the upwards direction, away from the X axis, it is increasing. If the line is above the X axis it also means it is going forward. Anything below the X axis is going backwards in the negative direction. The closer the line is to the X axis, the slower it is moving. The steeper the slope is, the faster the object is going.
Interpreting Velocity vs Time and Acceleration vs Time:
The acceleration versus time graph's directly relates to the velocity versus time graph. If you are given one of these graphs, you can look and identify to make the coinciding graph.
All of the velocity versus time graphs on the left have a positive slope, so therefore that acceleration versus time graphs have positive acceleration. On the right, all of the velocity versus time graph's have a negative slope, so they also will have a negative acceleration on the coinciding A vs T graphs. On the far right the velocity is constant but the slope is zero, therefore it has an acceleration of zero.
Velocity vs Time Graphs:
·
To show a constant velocity, a straight
horizontal line will be drawn.
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If the graph has a positive slope, then the
velocity is increasing. If the graph has a negative slope, then the velocity is
decreasing.
·
In V vs T graphs, the X axis is referred to as
the origin. The farther away from the X axis, the faster the object is moving.
The closer the object is to the X axis, the slower it is moving.
·
The area above the origin represents the
positive side of the graph, which indicates an object is moving forward. The
area under the X axis (negative side) indicates that the object is moving
backward.
Acceleration:
The rate of change in the velocity of a given object. The
slope of a graph shows the acceleration. Acceleration can be calculated by:
1.
Finding the slope on a velocity vs time graph.
2.
2. Using the formula A=(1/2)bh +l x w
3.
Find the constant acceleration or instantaneous
velocity by: V= at + V^0
4. a= Delta V
Delta T (change in)
Acceleration vs Time Graphs:
·
These graphs tell us the acceleration of an
object and if it is in the positive or negative direction, and tells us the
slope that would be depicted on an V vs T graph.
·
If a line is straight, it shows a constant
velocity.
·
The Y intercept in a A vs T graph tells us the
starting position.
·
The area underneath the line tells us the change
in velocity. By calculated the area underneath the line you can find the change
in X, also known as Delta X.
·
In an A vs T graph, you cannot determine the
objects position.
Position vs Time Graphs:
How is the CAPM applicable to real life?Acceleration is commonly associated with speed, particularly when driving a car. In class, we often do problems that have to do with the acceleration it would take for a car to come to a complete stop for the amount of time it would take a driver to reach a certain speed. This unit has also taught us the scale of being able to predict any point on the graph that a line will intersect with if it has a constant velocity and starting point. Being able to make predictions and draw conclusions from graphs and other visual aids is a crucial skill that is a necessity in most business settings.
