1D Kinematics

Introduction

• Kinematics is the branch of physics that deals with the motion of objects without considering the forces causing the motion.

• 1D kinematics focuses on the motion of objects in a straight line.

Key Concepts

1. Displacement:

   • The change in position of an object.

   • It is a vector quantity, represented by Δx.

   • Δx = xf - xi, where xf is the final position and xi is the initial position.

2. Velocity:

   • The rate of change of displacement.

   • It is a vector quantity, represented by v.

   • v = Δx / Δt, where Δt is the change in time.

3. Speed:

   • The rate of change of distance.

   • It is a scalar quantity, represented by s.

   • s = |Δx / Δt|, where | | denotes magnitude.

4. Acceleration:

   • The rate of change of velocity.

   • It is a vector quantity, represented by a.

   • a = Δv / Δt, where Δv is the change in velocity.

Equations

1. Constant Velocity:

   • Δx = v * Δt

2. Average Velocity:

   • v_avg = Δx / Δt

3. Constant Acceleration:

   • Δx = v_i * Δt + (1/2) * a * Δt^2

   • v_f = v_i + a * Δt

   • Δx = (v_f^2 - v_i^2) / (2 * a)

4. Free Fall:

   • Δx = v_i * Δt + (1/2) * g * Δt^2

   • v_f = v_i + g * Δt

   • Δx = (v_f^2 - v_i^2) / (2 * g)

Graphical Representations

1. Position-Time Graph:

   • Shows how an object's position changes over time.

   • Slope represents velocity.

2. Velocity-Time Graph:

   • Shows how an object's velocity changes over time.

   • Slope represents acceleration.

Conclusion

• 1D kinematics provides a framework to analyze the motion of objects in a straight line.

• Displacement, velocity, speed, and acceleration are key concepts in 1D kinematics.