Unit 1: Kinematics

Executive Summary

Kinematics describes motion without asking what causes it: position, velocity, and acceleration in one and two dimensions.

The big three quantities

Position $x$ (m), velocity $v = \frac{\Delta x}{\Delta t}$ (m/s), and acceleration $a = \frac{\Delta v}{\Delta t}$ (m/s²) are linked by slopes and areas. On a position-time graph, slope = velocity. On a velocity-time graph, slope = acceleration and the area under the curve = displacement.

Constant-acceleration equations

For constant $a$: $v = v_0 + at$, $x = x_0 + v_0 t + \frac{1}{2}at^2$, $v^2 = v_0^2 + 2a\Delta x$. Free fall is just constant acceleration with $a = -g$ (take down as negative or positive — be consistent).

Two dimensions

Projectile motion splits into independent horizontal (constant velocity) and vertical (constant acceleration) parts. The horizontal range depends on both launch speed and angle; max height uses the vertical component alone. Relative velocity adds vectors: $\vec{v}_{AB} = \vec{v}_{AC} + \vec{v}_{CB}$.

Exam traps

Velocity and speed differ (speed = magnitude). Acceleration can be nonzero even when speed is constant (direction change). Area under a v-t graph is DISPLACEMENT, not distance. At a projectile's peak, vertical velocity is zero but acceleration is still $g$.