One-Dimensional Motion Fundamentals

Chapter 2: Motion in One Dimension — Revision Sheet

1. 📌 Essentials

• Motion along a straight line described by position, velocity, and acceleration.
• Displacement ($\Delta x$): change in position, a vector quantity.
• Distance: total path length traveled, scalar.
• Average velocity: $\displaystyle v_{avg} = \frac{\Delta x}{\Delta t}$.
• Instantaneous velocity: $\displaystyle v(t) = \frac{dx}{dt}$.
• Average acceleration: $\displaystyle a_{avg} = \frac{\Delta v}{\Delta t}$.
• Instantaneous acceleration: $\displaystyle a(t) = \frac{dv}{dt}$.
• Equations of motion (constant acceleration):
  • $\displaystyle v = v_i + a t$
  • $\displaystyle x = x_i + v_i t + \frac{1}{2} a t^2$
  • $\displaystyle v^2 = v_i^2 + 2 a (x - x_i)$
• Free fall: acceleration due to gravity, $a = -g = -9.80\, m/s^2$.
• At maximum height, vertical velocity is zero.
• Symmetry in projectile motion: ascent time = descent time.

2. 🧩 Key Structures & Components