====== Kinematic Equations ====== * $V = \frac{\Delta \text{position}}{\Delta \text{time}}$((displacement is the change in position, and velocity is that over time)) * $V_f = V_i + at$ * $V_f^2 = V_i^2+2aD$ * $D = V_it + \frac{1}{2}at^2$ * $D = V_ft - \frac{1}{2}at^2$ * $D = \frac{1}{2}(V_f + V_i)t$ Take note of the missing variable for each equation, these don't have to be memorized since they are clearly derived from one root function. ===== Definitions ===== ==== Vector ==== A vector quantity includes direction within its value. Acceleration and Velocity are vector quantities. ==== Scalar ==== Scalar quantities don't, speed is the obvious one. ==== Free Fall ==== When an object is in free fall, gravity is the only force affecting the object. Useful for narrowing forces for calculation. ===== Example ===== > A car starts at rest and accelerates at **3 m/s^2** for **8 seconds**. How far did it go? ==== Variables ==== * $V_i = 0$ m/s * $a = 3$ m/s^2 * $t = 8$ seconds ==== Equation(s) ==== * $D = V_it + \frac{1}{2}at^2$ - $D = 0(8) + \frac{1}{2}3(8^2)$ - $D = 0 + 96$ - $\boxed{D = 96 m}$ * $V_f = V_i + at$ - $V_f = 0 + 3(8)$ - $\boxed{V_f = 24 m/s}$