Kinematics

The Big Five Equations

Uniformly accelerated motion is fully described by five interchangeable equations; choose the one whose variables match what the problem gives: $v = v_0 + at$ $\Delta x = v_0t + \tfrac{1}{2}at^2$ $v^2 = v_0^2 + 2a\Delta x$ Distinguish vectors (displacement, velocity, acceleration) from scalars (distance, speed), and read velocity-time graphs: slope is acceleration, area is displacement.

Free Fall and Projectiles

All objects fall with the same acceleration $g \approx 10\ \text{m/s}^2$ (MCAT-friendly rounding) regardless of mass. Projectile motion separates into independent components: horizontal velocity $v_x = v_0\cos\theta$ is constant, while vertical motion accelerates at $-g$. Time of flight comes entirely from the vertical equations, and range is $R = \frac{v_0^2\sin(2\theta)}{g}$ maximized at 45 degrees. At the peak, vertical velocity is zero but acceleration is still $g$.

Relative Motion

For one-dimensional chase and river problems, subtract velocities directly: $v_{A/B} = v_A - v_B$. This converts meeting-time questions into a single closing-speed calculation.

Key Takeaways

• Pick the Big Five equation missing the variable you don't know or need.
• Horizontal and vertical projectile motion never mix; time links them.
• $v = 0$ at the top of a trajectory, but $a = g$ always.
• Use $g = 10\ \text{m/s}^2$ for fast arithmetic.