CAPM Unit SUmmary

CAPM Unit Summary:

•       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.

·      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.