1. Calculus In Physics
By: May Cheung

2. One-Dimensional Motion
Examples:
a car moving on a straight road
a person walking down a hallway
a sprinter running on a straight race course
dropping a pencil
throwing a ball straight up
a glider moving on an air track
and many others...

3. Derivatives
The position graph  s(t), where x is time and the y is distance
The velocity graph  v(t), is the derivative of the position graph, based on how quickly the distance is changing
The acceleration graph  a(t), is the derivative of the velocity graph, based on how quickly the velocity is changing

4. Position This graph records the distance that is travel
Let’s use the example of a person that is walking
the distance either increases or decreases relative to where the starting point is but to make things easier right (forward) is positive and left (backward) is negative

5. Velocity
this graph based on the slope of the position graph meaning how slow or how fast the person is traveling
A positive slope – the person is walking to the right and the distance is increasing
An increase in the positive slope - the person is walking faster so the distance is increasing at a faster rate
A decrease in the positive slope – the person is walking slower so the distance is increasing at a slower rate
Zero slope – the person has walking and no distance has been traveled

6. Cont.
Zero slope – the person has stopped and no distance has been traveled
A negative slope - the person is walking in the negative direction (left) so the distance is decreasing
An increase in the negative slope – the person is walking faster in the left direction so the distance is decreasing at a faster rate
An decrease in the negative slope – the person is walking slower in the left direction so the distance is decreasing at a slower rate

7. Acceleration
This graph is based on the slope of the velocity meaning how fast or how slow the person is changing his pace
For example : walking to walking faster as opposed to walking to running
a positive slope – the person changes from walking to running, increasing the pace of its travel at a exponential pattern (3 ft/sec to 9 ft/sec to 81 ft/sec)
Zero slope – the person changes from walking to walking faster at a consistent pattern (2 ft/sec to 4 ft/sec to 6 ft/sec)
a negative slope – the person changes from running to walking, decreasing the pace of its travel at an exponential pattern (81 ft/sec to 9 ft/sec to 3 ft/sec)