AP Physics 1 - Unit 1: Kinematics

1.1 Scalars and Vectors in one dimension

Vector Quantity: includes & considers both magnitude and direction (±/-)
Scalar Quality: considers only magnitude

Examples:

Vectors - velocity, displacement, force

Scalars - speed, mass, energy, distance

Net force is all the forces put together

Force is measured by the Newtons unit (N)

X-axis and Y-axis forces cannot be combined

1.2 Displacement, Velocity, and Acceleration

Displacement: Change in position (vector)

$\Delta x=x_{f}-x_{i}$

$\Delta x$ , displacement

$x_{f}$ , final position

$x_i$ , initial position

Average speed: the average of how fast an object is moving (scalar)

$speed_{avg}=\frac{d}{\Delta t}$

$d$ , distance

$\Delta t$ , change in time

Average velocity: average of how fast an object is moving (vector)

$V_{avg}=\frac{\Delta x}{\Delta t}$

Average acceleration: average change in velocity (vector)

$A_{avg}=\frac{\Delta v}{\Delta t}$

Kinematic Equations represent the movement of an object

1.3 Representing Motion

Dot Diagram: visual way to represent motion over time

Dots are spread out evenly: Constant velocity

Dots get further away: Object is speeding up

Dots get closer apart: Object is slowing down

Kinematic Equations:

(memorization not necessary)

$v_{f}=v_0+at$

$x_{f}=x_0+v_0t+\frac12at^2$
$v_{f}^2=v_0^2+2a\left(x_{f}-x_{i}\right)$

To solve motion problems:

identify known
identify unknown
select appropriate equation
solve algebraically

Kinematics can only be applied directly if the acceleration is constant

Free fall: when an object moving only under the influence of gravity

The acceleration of an object under free fall is -9.8m/s² or -10m/s²

To graph in free fall;

Acceleration - straight line

Velocity - linear negative slope

Displacement - parabola

1.4 Reference Frames and Relative Motion

A frame of reference: point of view from how we view motions and interactions

To solve for relative motion:

$motion_{ab}=motion_{a}-motion_{b}$

For multiple points:

$motion_{ac}=motion_{ab}-motion_{bc}$

1.5 Vectors and Motion in 2D

One dimensional object: moves on either only the x-axis or y-axis

Two dimensional object: moves on both the x-axis and y-axis, has both components

To find the resultant vector, use Pythagorean Theorem:

$c=\sqrt{a^2+b^2}$

To find its direction or angle:

$\theta=\tan^{-1}\left(\frac{opp}{adj}\right)$

Projectiles: move under the influence of gravity only, but at an angle

Projectiles follow a parabolic path and have motion in both directions;

Horizontal Motion:

$a=g$

$\upsilon_0=0$ m/s

$\Delta y=\frac12gt^2$

Vertical Motion:

$a=0$

$v_0=v$

$\Delta x=vt$

Velocity at the highest point in a projectile will be 0