Equations of Motion: A Brief Overview

Equations of motion are mathematical expressions that describe the relationship between an object's position and velocity, acceleration, and time. They are fundamental to understanding the behavior of moving objects.

Equations of Motion for Constant Acceleration

When an object moves with constant acceleration, the following equations can be used to describe its motion:

1. Velocity-Time Equation:

  • Equation: v = u + at

  • Variables:

    • v: Final velocity

    • u: Initial velocity

    • a: Acceleration

    • t: Time

2. Displacement-Time Equation:

  • Equation: s = ut + (1/2)at²

  • Variables:

    • s: Displacement

    • u: Initial velocity

    • a: Acceleration

    • t: Time

3. Velocity-Displacement Equation:

  • Equation: v² = u² + 2as

  • Variables:

    • v: Final velocity

    • u: Initial velocity

    • a: Acceleration

    • s: Displacement

Equations of Motion for Variable Acceleration

When acceleration is not constant, these equations can be used:

  • Velocity as a function of time: v = ∫a(t) dt + C

  • Displacement as a function of time: s = ∫v(t) dt + C

Key Points:

  • These equations are derived from the definitions of velocity, acceleration, and displacement.

  • They are useful for solving problems involving motion in one dimension.

  • The choice of which equation to use depends on the given information and the desired unknown quantity.

By understanding and applying these equations of motion, you can analyze the motion of objects and solve various problems in physics and engineering.