Kinematic equations for one-dimensional motion with constant acceleration

a_x = (v_xf - v_xi)/∆t, where ∆t = (t_f - t_i).
v_xf = v_xi + a_x ∆t.
v_x(avg) = (v_xf + v_xi)/2.
x_f - x_i = v_xi∆t + ½a_x∆t².
v_xf² = v_xi² + 2a_x(x_f - x_i).

Kinematic equations for three-dimensional motion with constant acceleration

v_x = v_0x + ∆v_x = v_0x + a_x∆t, 
v_y = v_0y + a_y∆t, 
v_z = v_0z∆t + a_z∆t,
or   v = v₀ + a∆t.

x = x₀ + v_0x∆t + ½a_x∆t²,
y = y₀ + v_0y∆t + ½a_y∆t²,
z = z₀ + v_0z∆t + ½a_z∆t²,   
or    r = r₀ + v₀∆t + ½a∆t².

Projectile motion

v_x = v₀cosθ₀ = constant,  x =  x₀ + v₀cosθ₀t,
v_y = v₀sinθ₀ - gt,  y = y₀ + v₀sinθ₀t - ½gt².
Trajectory:  y = y₀ + (x - x₀)tan(θ₀) - g(x - x₀)²/(2v₀²cos²(θ₀)).
Range:  R = (v₀²sin2θ₀)/g.

Uniform circular motion:

Centripetal acceleration: a_c = v²/r.
Centripetal force: F = mv²/r

Friction and drag

Friction:  f_s ≤ μ_sN,  f_k= μ_kN
Drag:  R = -bv (low speed),  R = ½CρAv² (high speed)