Kinematics Formula Sheet

Cheatsheet Content

Kinematics Formula Sheet Position Functions: $x(t)$ and $y(t)$ Velocity Function: $v(t)$ Acceleration Function: $a(t)$ Displacement $d = \Delta x = x_f - x_0$ Average Velocity $\bar{v} = \frac{\text{displacement}}{\text{time}} = \frac{\Delta x}{\Delta t} = \frac{x_2 - x_1}{t_2 - t_1}$ Average Speed $\bar{s} = \frac{\text{total distance}}{\text{elapsed time}}$ Instantaneous Velocity $v(t) = \frac{d}{dt} [x(t)]$ Instantaneous Speed $s(t) = |v(t)|$ Average Acceleration $\bar{a} = \frac{\Delta v}{\Delta t} = \frac{v_f - v_0}{t_f - t_0}$ Instantaneous Acceleration $a(t) = \frac{d}{dt} [v(t)] $ Constant Speed $d = vt$ $x_f = x_0 + vt$ Definitions for Constant Motion Displacement: $d = \Delta x$ Final Position: $x_f$ Initial Position: $x_0$ Final Velocity: $v_f$ Initial Velocity: $v_0$ Time: $t$ Constant Acceleration $\bar{v} = \frac{v_f + v_0}{2}$ $v_f = v_0 + at$ $v_f^2 = v_0^2 + 2ad$ $d = \frac{1}{2} [v_0 + v_f]t$ $x_f = x_0 + v_{x0}t + \frac{1}{2}at^2$ $y_f = y_0 + v_{y0}t + \frac{1}{2}at^2$ Gravitational Acceleration $g = -9.8 \text{ m/s}^2$