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).

Projectile motion

vx = v0x,  ∆x = v0xt,  vy = v0y - gt,  y = y0 + v0yt - gt2.

Hooke's law

F = -kx

Work, energy and power

W = Fd ,
The work done by a force can be positive or negative.  If the component of the force in the direction of the displacement is positive, the work is positive, and if the component of the force in the direction of the displacement is negative, the work is negative.
Kinetic energy: K = mv2.
Gravitational potential energy: Ug = mgh (with ground as reference).
Elastic potential energy: Us = kx2.
P = ∆W/∆t

Friction

fs≤ μsN, fk = μkN.

Uniform circular motion:

Centripetal acceleration: ac = v2/r.
Centripetal force: Fc = mv2/r.