Equations of Motion

Equations of Motion

Introduction

• The equations of motion are fundamental tools in physics used to describe the motion of objects.
• They relate various parameters like initial velocity, final velocity, acceleration, time, and displacement to analyse an object's motion.

Key Quantities

• Initial Velocity (u): The object's velocity at the beginning of motion.
• Final Velocity (v): The object's velocity at a specific point in time.
• Acceleration (a): The rate of change of velocity.
• Time (t): The duration for which the motion occurs.
• Displacement (s): The change in position of the object.

Nature of Quantities

• u, v, a, and s are vector quantities as they have both magnitude and direction.
• Time (t) is a scalar quantity as it only has magnitude.

Equations

• If any three of the five quantities are known, the other two can be calculated using the following equations:

Equation for Final Velocity (v):

• v = u + at
• Calculates the final velocity when initial velocity, acceleration, and time are known.

Equation for Displacement (s):

• s = ut + (1/2)at^2
• Computes the displacement when initial velocity, time, and acceleration are known.

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Physics

Equations of Motion

Equation for Final Velocity (v) Squared:

• v^2 = u^2 + 2as
• Finds the final velocity squared when initial velocity, acceleration, and displacement are known.

Equation for Displacement (s) with Average Velocity:

• s = (u + v)t/2
• Determines displacement using the average velocity, initial velocity, final velocity, and time.

Conditions for Application

• The equations of motion are valid for objects moving in a straight line with constant acceleration.
• They provide accurate results for a wide range of motion scenarios.

Summary

• Equations of motion are essential tools in physics for analysing object motion.
• They involve key quantities like initial and final velocity, acceleration, time, and displacement.
• These equations allow us to calculate unknown parameters based on known values.
• Applicable when an object moves in a straight line with constant acceleration.