AP®︎ Physics 1: Unit 1 Practice Test

Essential Knowledge: 1.1.A.1

Scalars are quantities described by magnitude only; vectors are quantities described by both magnitude and direction.

Essential Knowledge: 1.1.A.2

Vectors can be visually modeled as arrows with appropriate direction and lengths proportional to their magnitude.

Essential Knowledge: 1.1.A.3

Distance and speed are examples of scalar quantities, while position, displacement, velocity, and acceleration are examples of vector quantities.

Essential Knowledge: 1.1.A.3.i

Vectors are notated with an arrow above the symbol for that quantity. Relevant equation: $\vec{v} = \vec{v}_0 + \vec{a}t$

Essential Knowledge: 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: $v_x = v_{x0} + a_xt$

Essential Knowledge: 1.1.B.1

When determining a vector sum in a given one-dimensional coordinate system, opposite directions are denoted by opposite signs.

Essential Knowledge: 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.

Essential Knowledge: 1.2.A.2

Displacement is the change in an object’s position. Relevant equation: $\Delta x = x - x_0$

Essential Knowledge: 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.

Essential Knowledge: 1.2.B.2

Average velocity is the displacement of an object divided by the interval of time in which that displacement occurs. Relevant equation: $\vec{v}_{avg} = \frac{\vec{\Delta x}}{\Delta t}$

Essential Knowledge: 1.2.B.3

Average acceleration is the change in velocity divided by the interval of time in which that change in velocity occurs. Relevant equation: $\vec{a}_{avg} = \frac{\vec{\Delta v}}{\Delta t}$

Essential Knowledge: 1.2.B.4

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

Essential Knowledge: 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.

Essential Knowledge: 1.3.A.1

Motion can be represented by motion diagrams, figures, graphs, equations, and narrative descriptions.

Essential Knowledge: 1.3.A.2

For constant acceleration, three kinematic equations can be used to describe instantaneous linear motion in one dimension: $v_x = v_{x0} + a_x t$; $x = x_0 + v_{x0}t + \frac{1}{2}a_x t^2$; $v_x^2 = v_{x0}^2 + 2a_x(x - x_0)$; 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.

Essential Knowledge: 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 $a_g = g \approx 10\ m/s^{2}$.

Essential Knowledge: 1.3.A.4

Graphs of position, velocity, and acceleration as functions of time can be used to find the relationships between those quantities.

Essential Knowledge: 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.

Essential Knowledge: 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.

Essential Knowledge: 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).

Essential Knowledge: 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.

Essential Knowledge: 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.

Essential Knowledge: 1.4.B.1

Measurements from a given reference frame may be converted to measurements from another reference frame.

Essential Knowledge: 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.

Essential Knowledge: 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.

Essential Knowledge: 1.4.B.2.ii

The acceleration of any object is the same as measured from all inertial reference frames.

Essential Knowledge: 1.5.A.1

Vectors can be mathematically modeled as the resultant of two perpendicular components.

Essential Knowledge: 1.5.A.2

Vectors can be resolved into components using a chosen coordinate system.

Essential Knowledge: 1.5.A.3

Vectors can be resolved into perpendicular components using trigonometric functions and relationships. Relevant equations: $\sin\theta = \frac{a}{c}$; $\cos\theta = \frac{b}{c}$; $\tan\theta = \frac{a}{b}$; $a^{2} + b^{2} = c^{2}$

Essential Knowledge: 1.5.B.1

Motion in two dimensions can be analyzed using one-dimensional kinematic relationships if the motion is separated into components.

Essential Knowledge: 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.