Describing Motion: Kinematics

Acceleration:

Velocity:

The instantaneous velocity has the same magnitude as instantaneous speed

Reference Frames

The idea of the Kinematic Equations stems from the fact that the acceleration is constant, which yields that the average acceleration is equal to the instanteneous acceleration.

It should be trivial to first get $v = u + at$, then using that along with

$$V_{avg} = \frac{(v_1+v_2)}{2}$$

$$V_{avg} = \frac{(\Delta X)}{t}$$

, we can get $\Delta X = v_1t + \frac{1}{2}at^2$