AP Mechanics Unit 1 – One Dimensional Kinematics
Objectives
General ideas
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Distinguish between vector and scalar quantities
Understand the concepts of position, displacement, velocity and acceleration
Use multiple representations of motion (graphical, verbal, and mathematical).
Distinguish between average and instantaneous velocity.
Distinguish between average speed and average velocity
1. You should be able to determine the average velocity of an object by:
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determining the slope of an x vs t graph.
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using the equation v 
x
t
v  vo
 using the equation v 
2
2. You should be able to determine the instantaneous velocity of an object by:
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determining the slope of the tangent to an x vs t graph at a given point.
Using an appropriate equation
3. You should be able to determine the displacement of an object by:
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finding the area under a v vs t graph.
Using an appropriate equation
4. You should be able to determine the acceleration of an object by:
 finding the slope of a v vs t graph
 Using an appropriate equation
5. Given an x vs t graph, you should be able to:
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describe the motion of the object (starting position, direction of motion, velocity)
draw the corresponding v vs t graph and a vs t graph
determine the average velocity or instantaneous velocity of the object.
Recognize the appropriate mathematical model that represents the curve
6. Given a v vs t graph, you should be able to:
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describe the motion of the object (direction of motion, how fast)
draw the corresponding x vs t graph and a vs t graph
determine the displacement of the object (area under curve).
determine the acceleration of the object (slope).
Recognize the appropriate mathematical model that represents the curve
7. Given an a vs t graph, you should be able to:
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describe the motion of the object (direction of acceleration, speeding up or slowing down)
draw the corresponding x vs t graph and v vs t graph
determine the change in velocity of the object (area under curve).
Recognize the appropriate mathematical model that represents the curve
8. Define what a derivative is and find derivatives of polynomials.
9. Find the derivative of position as a function of time to determine velocity as a function of time.
10. Find the derivative of velocity as a function of time to determine acceleration as a function of
time
11. Define what an integral is:
a. as the anti-derivative of a function, i.e. what is the function whose derivative is…?
(Indefinite integral)
b. as the area under a curve between two points (definite integral) and find integrals
of polynomials
12. Distinguish between the indefinite and definite integrals
13. Find the indefinite integral of velocity as a function of time to determine position as a
function of time.
14. Find the definite integral of velocity between two times in order to determine the
displacement of an object.
15. Find the indefinite integral of acceleration as a function of time to determine velocity as a
function of time.
16. Find the definite integral of acceleration between two times in order to determine the change
in velocity of an object.
17. Relate the concepts of integrals and derivatives to graphs.
a. Slope of the line tangent to a curve is the derivative of the function at that point
b. Area under a curve is the integral of that function.
18. Realize that all motion is relative to a frame of reference
19. Determine the velocity of an object in a reference frame given the velocity of the object in
another reference frame and the velocity of the reference frame.
Textbook Reference: Chapter 2
Other References: Calculus Packet