Understanding Kinematics: Motion Basics

Kinematics Overview

• Kinematics is the study of the motion of objects without considering the forces that cause the motion.
• It is a branch of classical mechanics in physics.
• It aims to predict motion using mathematical models (equations) with known or measured values.

Core Values of Motion

• Position describes the location of an object relative to a reference point.
• A reference point is a chosen location to determine an object's position.
• Coordinate axes define a frame of reference, with the origin as the reference point.
• Positions are indicated on a coordinate axis with a numerical measurement and direction.

Displacement vs. Distance

• Displacement is a measure of the change in position in a straight line; it is a vector quantity.
• Distance is the total length traveled by an object, which is a scalar quantity.
• For example, traveling to a restaurant 1 km away and returning back halfway gives a distance of 1.5 km and a displacement of 500 meters.

Velocity

• Velocity is the rate of change of position and is a vector quantity.
• High velocity means a significant change in an object's position over a short time, signifying a fast object.
• Low velocity means a small change in an object's position over a long time, signifying a slow object.
• Velocity is calculated by dividing displacement (change in position) by the time taken, measured in meters per second (m/s).

Velocity vs. Speed

• Speed is the rate of distance traveled over a period of time and is a scalar quantity.
• Velocity uses displacement in its calculation, while speed uses distance.
• Both velocity and speed are measured in meters per second.

Instantaneous vs. Average Velocity/Speed

• Instantaneous velocity/speed indicates how fast an object is moving at a specific moment.
• A car speedometer is an example of instantaneous speed.
• Measuring instantaneous velocity requires a very small displacement over a very small period of time.
• Average velocity/speed measures the rate of travel over an entire journey.
• A car's average velocity might be 5 km/h over 30 minutes, while its instantaneous velocity changes due to traffic.

Acceleration

• Acceleration is the rate of change of velocity and is a vector quantity.
• A change in velocity (increasing or decreasing) indicates acceleration.
• Decreasing velocity corresponds to slowing down.
• Increasing velocity corresponds to speeding up.
• Acceleration is derived by dividing the change in velocity by the time taken, measured in meters per second squared (m/s²).

SUVAT Equations (Kinematic Equations)

• SUVAT equations model motion to predict unknown values.
• They use displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t).
• Four SUVAT equations are used with known information to find unknown values.
• These equations apply only to objects with uniform (constant) acceleration.

Uniform vs. Non-Uniform Acceleration

• Uniform acceleration means the acceleration of the object remains constant.
• Non-uniform acceleration means the acceleration is changing.
• A runner on a hilly path, objects moving in circles, and objects experiencing air resistance are examples of non-uniform acceleration.
• Problem-solving requires consideration of uniform motion and whether air resistance is ignored because SUVAT equations apply only to uniform acceleration.

Projectile Motion

• Projectiles move in vertical and horizontal dimensions, creating a parabolic path.
• Horizontal and vertical motions are independent.
• Calculations for vertical and horizontal motion can be performed separately.

Projectile Motion Without Fluid Resistance

• Without air resistance, horizontal motion has a uniform acceleration of zero.
• Vertical motion has a uniform acceleration of -9.81 m/s² due to gravity.
• SUVAT equations can be used to find displacement, time, and velocities.

Projectile Motion With Fluid Resistance

• Air resistance reduces horizontal acceleration, decreasing the object's velocity over time and shortening the range (horizontal displacement).
• Air resistance affects vertical motion in complex ways.
• As an object moves upwards, air resistance increases downward acceleration, causing it to slow down more quickly.
• As an object moves downwards, air resistance pushes upward, reducing downward acceleration.
• Air resistance reduces flight time and vertical height.

Terminal Speed

• Objects falling for enough time or having a large surface area will reach terminal speed.
• Terminal speed occurs when an object stops accelerating downward and moves at a constant velocity.
• Terminal speed is reached when the force from air resistance equals the force of gravity.