Formulas 1

Kinematic equations for one-dimensional motion with constant acceleration

ax = (vxf - vxi)/∆t, where ∆t = (tf - ti).
vxf = vxi + ax ∆t.
vx(avg) = (vxf + vxi)/2.
xf - xi = vxi∆t + ax∆t2.
vxf2 = vxi2 + 2ax(xf - xi).

Kinematic equations for three-dimensional motion with constant acceleration

vx = v0x + ∆vx = v0x + ax∆t, 
vy = v0y + ay∆t, 
vz = v0z∆t + az∆t,
or   v = v0 + a∆t.

x = x0 + v0x∆t + ax∆t2,
y = y0 + v0y∆t + ay∆t2,
z = z0 + v0z∆t + az∆t2,   
or    r = r0 + v0∆t + a∆t2.

Projectile motion

vx = v0cosθ0 = constant,  x =  x0 + v0cosθ0t,
vy = v0sinθ0 - gt,  y = y0 + v0sinθ0t - gt2.
Trajectory:  y = y0 + (x - x0)tan(θ0) - g(x - x0)2/(2v02cos20)).
Range:  R = (v02sin2θ0)/g.

Uniform circular motion:

Centripetal acceleration: ac = v2/r.