1 Kinematics

Describe a scalar or vector quantity using magnitude and direction, as appropriate.

• Scalars are quantities described by magnitude only; vectors are quantities described by both magnitude and direction.
• Vectors can be visually modeled as arrows with appropriate direction and lengths proportional to their magnitude.
• Distance and speed are examples of scalar quantities, while position, displacement, velocity, and acceleration are examples of vector quantities.
• Vectors can be expressed in unit vector notation or as a magnitude and a direction.
  • i. Unit vector notation can be used to represent vectors as the sum of their constituent components in the x-, y-, and z-directions, denoted by i, j, and k, respectively. Relevant equation:
  • ii. The position vector of a point is given by r, and the unit vector in the direction of the position vector is denoted r. TOPIC 1.1 Scalars and Vectors Kinematics UNIT 1
  • iii. A resultant vector is the vector sum of the addend vectors’ components. Relevant equations:
• In a given one-dimensional coordinate system, opposite directions are denoted by opposite signs.

Describe a change in an object’s position.

• When using the object model, the size, shape, and internal configuration are ignored. The object may be treated as a single point with extensive properties such as mass and charge.
• Displacement is the change in an object’s position. Relevant equation:

Describe the average velocity and acceleration of an object.

• Averages of velocity and acceleration are calculated considering the initial and final states of an object over an interval of time.
• Average velocity is the displacement of an object divided by the interval of time in which that displacement occurs.
• Average acceleration is the change in velocity divided by the interval of time in which that change in velocity occurs.
• An object is accelerating if either the magnitude and/or direction of the object’s velocity are changing. TOPIC 1.2 Displacement, Velocity, and Acceleration
• Calculating average velocity or average acceleration over a very small time interval yields a value that is very close to the instantaneous velocity or instantaneous acceleration.

Describe the instantaneous position, velocity, and acceleration of an object as a function of time.

• As the time interval used to calculate the average value of a quantity approaches zero, the average value of that quantity approaches the value of the quantity at that instant, called the instantaneous value.
  • i. Instantaneous velocity is the rate of change of the object’s position, which is equal to the derivative of position with respect to time. Relevant equations:  dr v= dt dxvx = dt
  • ii. Instantaneous acceleration is the rate of change of the object’s velocity, which is equal to the derivative of velocity with respect to time. Relevant equations:  dv a= dt dvax = x dt
• Time-dependent functions and instantaneous values of position, velocity, and acceleration can be determined using differentiation and integration.

Describe the position, velocity, and acceleration of an object using representations of that object’s motion.

• Motion can be represented by motion diagrams, figures, graphs, equations, and narrative descriptions.
• For constant acceleration, three kinematic equations can be used to describe instantaneous linear motion in one dimension: vvxx=+ 0 atx vv2 xx=+ 2 0 2axx () −x 0 1xx =+00 vtxx +at 2 2 Note: The equations above are written to indicate motion in the x-direction, but these equations can be used in any single dimension as appropriate.
• Near the surface of Earth, the vertical acceleration caused by the force of gravity is downward, constant, and has a measured value approximately equal to
• Graphs of position, velocity, and acceleration as functions of time can be used to find the relationships between those quantities. TOPIC 1.3 Representing Motion
  • i. An object’s instantaneous velocity is the rate of change of the object’s position, which is equal to the slope of a line tangent to a point on a graph of the object’s position as a function of time. Relevant equation: dxvx = dt
  • ii. An object’s instantaneous acceleration is the rate of change of the object’s velocity, which is equal to the slope of a line tangent to a point on a graph of the object’s velocity as a function of time. Relevant equation: dva x x = dt
  • iii. The displacement of an object during a time interval is equal to the area under the curve of a graph of the object’s velocity as a function of time (i.e., the area bounded by the function and the horizontal axis for the appropriate interval). Relevant equation: 1
  • iv. The change in velocity of an object during a time interval is equal to the area under the curve of a graph of the acceleration of the object as a function of time. Relevant equation: BOUNDARY STATEMENT AP Physics C: Mechanics and AP Physics C: Electricity and Magnetism expects that for all situations in which a numerical quantity is required for g, the value g 10 m/ s2 will be used. However, students will not be penalized for correctly using the more precise commonly accepted values of g= 9.81 m/ s2 or g= 9. 8m /s2.

Describe the reference frame of a given observer.

• The choice of reference frame will determine the direction and magnitude of quantities measured by an observer in that reference frame.

Describe the motion of objects as measured by observers in different inertial reference frames.

• Measurements from a given reference frame may be converted to measurements from another reference frame.
• The observed velocity of an object results from the combination of the object’s velocity and the velocity of the observer’s reference frame.
  • i. Combining the motion of an object and the motion of an observer in a given reference frame involves the addition or subtraction of vectors.
  • ii. The acceleration of any object is the same as measured from all inertial reference frames. TOPIC 1.4 Reference Frames and Relative Motion

Describe the motion of an object moving in two or three dimensions. TOPIC 1.5 Motion in Two or Three Dimensions TOPIC 2.1 Systems and Center of Mass

• Motion in two or three dimensions can be analyzed using one-dimensional kinematic relationships if the motion is separated into components.
• Velocity and acceleration may be different in each dimension and may be nonuniform.
• Motion in one dimension may be changed without causing a change in a perpendicular dimension.
• Projectile motion is a special case of twodimensional motion that has zero acceleration in one dimension and constant, nonzero acceleration in the second dimension.