Kinematics · ⁨קינמטיקה⁩

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

• 1.1.A.1 Scalars are quantities described by magnitude only; vectors are 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 quantities, 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.
    • Equation: $\vec{v} = \vec{v}_0 + \vec{a}t$
  • 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.
    • Derived equation: $v_x = v_{x0} + a_x t$

Learning Objective 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.

Learning Objective 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.
  • Equation: $\Delta x = x - x_0$

Learning Objective 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 of time.
• 1.2.B.2 Average velocity is the displacement of an object divided by the interval of time in which that displacement occurs.
  • Equation: $\vec{v}_{avg} = \dfrac{\Delta \vec{x}}{\Delta t}$
• 1.2.B.3 Average acceleration is the change in velocity divided by the interval of time in which that change in velocity occurs.
  • Equation: $\vec{a}_{avg} = \dfrac{\Delta \vec{v}}{\Delta t}$

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

• 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 or instantaneous acceleration.

Learning Objective 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:
  • Equation: $v_x = v_{x0} + a_x t$
  • Equation: $x = x_0 + v_{x0}t + \dfrac{1}{2}a_x t^2$
  • Equation: $v_x^2 = v_{x0}^2 + 2a_x(x - x_0)$
  • 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.
• 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 $a_g = g \approx 10 \ m/s^2$.
• 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.

Boundary statement: AP Physics 1 does not expect students to quantitatively analyze nonuniform acceleration. However, students will be expected to be able to qualitatively analyze, sketch appropriate graphs of, and discuss situations in which acceleration is nonuniform.

Boundary statement: For all situations in which a numerical quantity is required for $g$, the value $g \approx 10 \ m/s^2$ will be used. However, students will not be penalized for correctly using the more precise commonly accepted values of $g = 9.81 \ \text{m/s}^2$ or $g = 9.8 \ \text{m/s}^2$.

Learning Objective 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.

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

• 1.4.B.1 Measurements 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.

Boundary statement: Unless otherwise stated, the frame of reference of any problem may be assumed to be inertial.

Boundary statement: Adding or subtracting vectors to find relative velocities is restricted to motion along one dimension for AP Physics 1.

Learning Objective 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.
  • Equation: $\sin \theta = \dfrac{a}{c}$
  • Equation: $\cos \theta = \dfrac{b}{c}$
  • Equation: $\tan \theta = \dfrac{a}{b}$
  • Equation: $a^2 + b^2 = c^2$

Learning Objective 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.
• 1.5.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 dimension.