Equation 1.1 solves for velocity, where \(\boldsymbol{v}\) is velocity, \(\Delta \boldsymbol{x}\) is displacement, and \(\Delta t\) is change in time

Equation 1.2 solves for speed, where \(\text{speed}\) is speed, \(\Delta d\) is change in displacement, and \(\Delta t\) is change in time

Equation 1.3 solves for acceleration, where \(a\) is acceleration, \(\Delta d\) is change in displacement, and \(\Delta t\) is change in time

Equation 1.1

$$\boldsymbol{v} = {\Delta \boldsymbol{x} \over \Delta t}$$

Equation 1.2

$$\text{speed} = {\Delta d \over \Delta t}$$

Equation 1.3

$$\boldsymbol{a} = {\Delta \boldsymbol{v} \over \Delta t}$$

Equation 1.3 can be modified to give us equation 2.6. To see the step by step process, view pages 37 through 38.

Equation 2.6 solves for final velocity, where \(\boldsymbol{v}\) is final velocity, \(\boldsymbol{v}_{\text{o}}\) is initial velocity, \(\boldsymbol{a}\) is acceleration, and \(t\) is final time.

Equation 1.1 can be modified to give us equation 2.15. To see the step by step process, view pages 40 through 41.

Equation 2.15 solves for final velocity, where \(\boldsymbol{v}\) is final velocity, \(\boldsymbol{v}_{\text{o}}\) is initial velocity, \(\boldsymbol{a}\) is acceleration, and \(\Delta \boldsymbol{x}\) is displacement.

Equation 2.19 solves for final velocity, where \(\Delta \boldsymbol{x}\) is displacement, \(\boldsymbol{v}_{\text{o}}\) is initial velocity, \(t\) is time, and \(\boldsymbol{a}\) is acceleration.

Equation 2.6

$$\boldsymbol{v} = \boldsymbol{v}_{\text{o}} + \boldsymbol{a} t$$

Equation 2.15

$$\boldsymbol{v}^2 = \boldsymbol{v}_{\text{o}}^2 + 2 \boldsymbol{a} \times \Delta \boldsymbol{x}$$

Equation 2.19

$$\Delta \boldsymbol{x} = \boldsymbol{v}_{\text{o}} t + {1 \over 2} \boldsymbol{a} t^2$$

Equation 3.2 calculates the magnitude of a vector, where \(A\) is the vector, \(A_x\) is the x-component, and \(A_y\) is the y-component.

Equation 3.3 calculates the direction of a vector, where \(\theta\) is the direction, \(A_x\) is the x-component, and \(A_y\) is the y-component.

Equation 3.6 calculates the y-component of a vector, where \(A\) is the magnitude, and \(A_y\) is the y-component.

Equation 3.7 calculates the x-component of a vector, where \(A\) is the magnitude, and \(A_x\) is the x-component.

It's important to note that the angle changes depending on the region it falls into. Below is a chart that shows what region a vector falls into, and what number to add to the direction based on the region.
Keep in mind that the angles have infinite precision.

Equation 3.2

$$\text{magnitude of } A = \sqrt{A^2_x + A^2_y}$$

Equation 3.3

$$\theta = \arctan({A_y \over A_x})$$

Equation 3.6

$$A_y = A \times \sin({\theta})$$

Equation 3.7

$$A_x = A \times \cos({\theta})$$