Rate Of Change Of Velocity

Key Notes:

Definition of Velocity:

  • Velocity refers to the speed of an object in a given direction.
  • It is a vector quantity, meaning it has both magnitude and direction.

Rate of Change of Velocity:

  • The rate of change of velocity is referred to as acceleration.
  • Mathematically, acceleration (aaa) is defined as:

a = Δv / Δta

where Δv is the change in velocity and Δt is the time interval.

Types of Acceleration:

  • Positive Acceleration: Velocity increases with time (e.g., a car speeding up).
  • Negative Acceleration (Deceleration): Velocity decreases with time (e.g., a car slowing down).
  • Zero Acceleration: Velocity remains constant.

Uniform Acceleration:

  • When the velocity of an object changes by an equal amount in equal intervals of time, the acceleration is uniform.
  • Example: A freely falling object under gravity has uniform acceleration ( 9.8 m/s2 ).

Non-Uniform Acceleration:

  • If the velocity changes by unequal amounts in equal time intervals, the acceleration is non-uniform.
  • Example: A car accelerating at varying speeds in traffic.

Units of Acceleration:

  • SI Unit: m/s2 (meters per second squared).

Graphical Representation:

  • Velocity-Time Graph:
    • The slope of the velocity-time graph gives the acceleration.
    • A straight line indicates uniform acceleration, while a curve indicates non-uniform acceleration.

Real-Life Examples:

  • A ball rolling down a slope (positive acceleration).
  • A cyclist applying brakes (negative acceleration).

Practical Applications:

  • Understanding the motion of vehicles.
  • Designing safe braking systems in cars.
  • Predicting motion in physics and engineering problems.

Key Formulae:

  • a = vf−vi / t​​, where:
    • vf​: Final velocity.
    • vi: Initial velocity.
    • t: Time taken.
  • Velocity under constant acceleration:

v = u + at

where u: Initial velocity, a: Acceleration, t: Time.

Let’s practice!