Physics Chapter on Equation of Motion

Equation of Motion: v = u + at

• Definitions:

  • v: Final velocity of the object (m/s)
  • u: Initial velocity of the object (m/s)
  • a: Acceleration (m/s²)
  • t: Time (s) during which the acceleration occurs

• Concepts:

  • This equation describes the relationship between initial velocity, final velocity, acceleration, and time for an object moving in a straight line under uniform acceleration.
  • It is applicable in linear motion scenarios where the acceleration is constant.

• Key Points:

  • If a = 0: The object moves at constant velocity, thus v = u.
  • If a > 0: The object speeds up (positive acceleration).
  • If a < 0: The object slows down (negative acceleration or deceleration).

• Rearranging the Equation:

  • To find acceleration: a = (v - u) / t
  • To find time: t = (v - u) / a
  • To find initial velocity: u = v - at

• Applications:

  • Used in solving problems related to freely falling objects, vehicles accelerating on a straight path, etc.
  • Helps in predicting the motion of objects when the initial conditions are known.

• Graphical Representation:

  • A velocity-time graph can be plotted where:
    • The slope represents acceleration (a).
    • The area under the graph represents the distance traveled.

• Example Problem:

  • If a car starts from rest (u = 0 m/s) and accelerates at 2 m/s² for 5 seconds, calculate final velocity (v).
    • v = u + at = 0 + (2 * 5) = 10 m/s.

• Units:

  • Ensure all quantities are in SI units for consistency (m/s for velocity, m/s² for acceleration, s for time).

Key Definitions

• v: Final velocity, measured in meters per second (m/s).
• u: Initial velocity, also measured in meters per second (m/s).
• a: Acceleration, measured in meters per second squared (m/s²).
• t: Time during which acceleration occurs, measured in seconds (s).

Fundamental Concepts

• The equation v = u + at expresses the relationship among initial velocity, final velocity, acceleration, and time for an object under uniform acceleration.
• Applicable to linear motion scenarios with constant acceleration.

Important Points

• When a = 0: The object maintains constant velocity, thus v = u.
• When a > 0: The object experiences positive acceleration, leading to an increase in speed.
• When a < 0: The object undergoes negative acceleration (deceleration), resulting in a decrease in speed.

Rearranging the Equation

• To determine acceleration: a = (v - u) / t
• To determine time: t = (v - u) / a
• To determine initial velocity: u = v - at

Practical Applications

• Useful in analyzing motion for freely falling objects, vehicles accelerating along a straight path, and similar scenarios.
• Provides a means to predict object motion based on known initial conditions.

Graphical Representation

• Velocity-time graphs illustrate motion characteristics:
  • The slope of the graph indicates acceleration (a).
  • The area beneath the graph represents the distance traveled by the object.

Example Problem

• A car starting from rest (u = 0 m/s) accelerates at 2 m/s² for 5 seconds.
• Calculate final velocity: v = u + at = 0 + (2 * 5) = 10 m/s.

Unit Consistency

• Ensure all quantities are expressed in SI units for accurate calculations:
  • Velocity in m/s
  • Acceleration in m/s²
  • Time in seconds (s)