Kinematics Equations

Constant velocity equation:

$v = \cfrac{\Delta x}{\Delta t}$

Equations for uniform acceleration:

$a = \cfrac{\Delta v}{\Delta t}$

$v = v_0 + at$

$\Delta x = {v_0}t + \cfrac{1}{2}at^2$

$v^2 = {v_0}^2 + 2a\Delta x$

$\bar{v} = \cfrac{\Delta x}{\Delta t}$

$\bar{v} = \cfrac{v + v_0}{2}$

$\Delta x = (\cfrac{v + v_0}{2}) \Delta t$

Acceleration due to gravity:
g = 9.8 m/s²
OR, g = 10 m/s² (if you round it up)

Where:

t = time (s)
x = position (m)
v = velocity (m/s)
a = acceleration (m/s²)

Δx = displacement = change in position = x – x₀
x₀ = initial position
Δv = change in velocity = v – v₀
= average velocity
v₀ = initial velocity

Δt = change in time = t – t₀
(often t₀=0 and therefore t = Δt)

Δ (Greek letter delta) means “change in.” Subtract the final and initial values to get the change in a variable.

“Before” and “after” values of a variable are notated in several ways in physics:

$\Delta x = x_f - x_i$
(“f” means final and “i” means initial)

$\Delta x = x - x_0$
(“x₀” means value of x at time=0, or the initial value of x, and “x” means value of x at a later time.)

$\Delta x = x^{\prime} - x$
( $x^{\prime}$ means x “prime” and means the value of x at a later time. Plain “x” is the initial value of x.)