Quick Recap — Graphs, Projectile & Circular Basics

  • Position-time graph: slope == velocity. Velocity-time graph: slope == acceleration, and the area under it == displacement.
  • Average velocity =displacementtime= \dfrac{\text{displacement}}{\text{time}}; it is zero whenever the body returns to its starting point.
  • Projectile: horizontal acceleration is zero, vertical acceleration is gg downward; the path is a parabola and the range is maximum at 45∘45^\circ.
  • Uniform circular motion: speed is constant but the velocity direction keeps changing; v=ωrv = \omega r, and the acceleration points toward the centre.