Chapter 3: Two Dimensional Kinematics

Kinematics

The study of motion without considering the forces causing it.

Two-dimensional kinematics

Deals with motion in a plane, considering both horizontal and vertical components.

Displacement

The change in position of an object.

$$\Delta r=r-r_{0}$$

Equation for displacement

Velocity

The rate of change of displacement.

Acceleration

The rate of change of velocity.

$$\overrightarrow{\overline{v}}=\dfrac{\Delta \overrightarrow{r}}{\Delta t}$$

Definition for average velocity

$$\overrightarrow{v}=\lim _{\Delta t\rightarrow 0}\dfrac{\Delta \overrightarrow{r}}{\Delta t}$$

Equation for instantaneous velocity

$$\overline{\overrightarrow{a}}=\dfrac{\Delta \overrightarrow{v}}{\Delta t}$$

Definition of average acceleration

$$\overrightarrow{a}=\lim _{\Delta t\rightarrow 0}\dfrac{\Delta \overrightarrow{v}}{\Delta t}$$

Equation for instantaneous accelerations

Projectile motion

The motion of an object launched into the air, moving under the influence of gravity.

Equations of Motion

Mathematical equations used to describe the motion of objects.

Divided into x and y components

Kinematic equations in two dimensions

Range

The horizontal distance covered by a projectile.

Maximum height

The highest point reached by a projectile.

-9.80 m/s²

a_y

0

a_x

Projectile motion

The motion of an object that is launched into the air and moves along a curved path under the influence of gravity.

Relative velocity

The velocity of an object or observer with respect to another object or observer.

$$\overrightarrow{v}_{AC}=\overrightarrow{v}_{AB}+\overrightarrow{v}_{BC}$$

Equation for relative velocity