Kinematics

Study of motion without considering the forces that cause it

Introduction to Motion

Kinematics is the branch of mechanics that describes the motion of objects without considering the forces that cause the motion. We focus on position, velocity, and acceleration as functions of time.

Key Concepts

  • Position (x): The location of an object relative to a reference point
  • Displacement (Δx): Change in position, a vector quantity
  • Velocity (v): Rate of change of position with respect to time
  • Acceleration (a): Rate of change of velocity with respect to time
Kinematic Equations

For motion with constant acceleration, we can use the following kinematic equations:

v = v₀ + at

Velocity as a function of time

x = x₀ + v₀t + ½at²

Position as a function of time

v² = v₀² + 2a(x - x₀)

Velocity-position relationship

x = x₀ + ½(v₀ + v)t

Average velocity equation

Where: v₀ = initial velocity, v = final velocity, a = acceleration, t = time, x₀ = initial position, x = final position

Two-Dimensional Motion

Motion in two dimensions can be analyzed by breaking it into horizontal (x) and vertical (y) components. Each component follows the one-dimensional kinematic equations independently.

Projectile Motion

A special case of 2D motion where an object moves under the influence of gravity alone. Key characteristics:

  • Horizontal velocity remains constant (no horizontal acceleration)
  • Vertical acceleration is constant: a_y = -g = -9.8 m/s²
  • Horizontal and vertical motions are independent
  • The trajectory forms a parabolic path
x = v₀ₓt

Horizontal position

y = v₀ᵧt - ½gt²

Vertical position

Projectile Motion Simulator
Launch projectiles at different angles and velocities. Observe the parabolic trajectory and analyze the motion in both horizontal and vertical components.
Max Height
15.94 m
Range
63.78 m
Flight Time
3.61 s
Graphical Analysis

Understanding motion graphs is crucial for analyzing kinematics problems:

Position-Time Graph

The slope represents velocity. A straight line indicates constant velocity, while a curved line shows changing velocity (acceleration).

Velocity-Time Graph

The slope represents acceleration. The area under the curve represents displacement.

Acceleration-Time Graph

The area under the curve represents the change in velocity.

Velocity-Time Graph Explorer
Manipulate velocity and acceleration to see how they affect motion. Watch the position change in real-time as you adjust the graph.
Current Time
0.00 s
Current Velocity
10.00 m/s
Displacement
0.00 m
Tip: The shaded area under the velocity-time curve represents the displacement. Notice how it changes as you adjust the initial velocity and acceleration!
Motion Diagram Builder
Create motion diagrams by placing position markers at equal time intervals. Visualize velocity and acceleration vectors.
How to use:
  • Click on the canvas to place position markers at equal time intervals
  • Purple vectors show velocity (displacement between positions)
  • Orange vectors show acceleration (change in velocity)
  • Green dot marks the starting position