AP Physics I - Topic #1 KInematics (1D and 2D) Learning Objectives

Learning Objectives:

1.1: Scalars and Vectors in One Dimension

1.1.A: Describe a scalar or vector quantity using magnitude and directions, as appropriate

1.1.A.1: Scalars are quantities described by magnitude only; vectors and quantities described by both

magnitude and direction

1.1.A.2: Vectors can be visually modeled as arrows with appropriate direction and lengths proportional

to their magnitude

1.1.A.3: Distance and speed are examples of scalar quantfities, while position, displacement, velocity,

and acceleration are examples of vector quantities.

1.1.A.3.I: Vectors are notated with an arrow above the symbol for that quantity (EQN: v = v0 +

at)

1.1.A.3.II: Vector notation is not required for vector components along an axis, in one

dimension, the sign of the component completely describes the direction of that component. (EQN: vx = vx0 + axt)

1.1.B: Describe a vector sum in one dimension

1.1.B.1: When determining a vector sum in a given one-dimensional coordinate system, opposite

directions are denoted by opposite signs.

1.2: Displacement, Velocity, and Acceleration

1.2.A: Describe a change in an object’s position

1.2.A.1: 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.

1.2.A.2: Displacement is the change in an object’s position (EQN: Δx = xf – x0)

1.2.B: Describe the average velocity and acceleration of an object

1.2.B.1: Averages of velocity and acceleration are calculated considering the initial and final states of an

object over an interval or time.

1.2.B.2: Average velocity is the displacement of an object divided by the interval of time in shich that

displacement occurs (EQN: vavg = Δx / Δt)

1.2.B.3: Average acceleration is the change in velocity divided by the interval of time in which that

change in velocity occurs (EQN: aavg = Δv / Δt)

1.2.B.4: An object is accelerating if the magnitude and/or direction of the object’s velocity are changing

1.2.B.5: Calculating average velocity or average acceleration over a very small time-interval yields a

value that is very close to the instantaneous velocity of instantaneous acceleration.

1.3: Representing Motion

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

1.3.A.1: Motion can be represented by motion diagrams, figures, graphs, equations, and narrative

descriptions

1.3.A.2: For constant acceleration, three kinematic equations can be used to describe instantaneous

linear motion in one dimension (EQN: vx = vx0 + axt) (EQN: xf = x0 + vx0t + ½ axt2) (EQN: vxf2 = vx02 + 2ax (xf –

x0). The equations are written to indicate motion in the s-direction, but these equations can be used in any single

dimension as appropriate.

1.3.A.3: 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 ag = g = 10 m/s2

1.3.A.4: Graphs of position, velocity, and acceleration as functions of time can be used to find the

relationships between those quantities.

1.3.A.4.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.

1.3.A.4.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.

1.3..A.4.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).

1.3.A.4.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.

1..4: Reference Frames and Relative Motion

1.4.A: Describe the reference frame of a given observer

1.4.A.1: The choice of reference frame will determine the direction and magnitude of quantities

measured by an observer in that reference frame.

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

1.4.B.1: Measurement from a given reference frame may be converted to measurements from another

reference frame.

1.4.B.2: The observed velocity of an object results from the combination of the object’s velocity and the

velocity of the observer’s reference frame.

1.4.B.2.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

1.4.B.2.II: The acceleration of any object is the same as measured from all inertial reference

frames.

1.5: Vectors and Motion in Two Dimensions

1.5.A: Describe the perpendicular components of a vector.

1.5.A.1: Vectors can be mathematically modeled as the resultant of two perpendicular components

1.5.A.2: Vectors can be resolved into components using a chosen coordinate system

1.5.A.3: Vectors can be resolved into perpendicular components using trigonometric functions and

relationships (EQN: sin θ = opposite / hypotenuse) (EQN: cos θ = adjacent / hypotenuse) (EQN: tan θ =

opposite / adjacent) (EQN: a2 + b2 = c2)

1.5.B: Describe the motion of an object moving in two dimensions.

1.5.B.1: Motion in two-dimensions can be analyzed using one-dimensional kinematic relationships if

the motion is separated into components

15.B.2: Projectile motion is a special case of two-dimensional motion that has zero acceleration in one

dimension and constant, nonzero acceleration in the second dimention