Kinematic and Angular Equations

General Kinematic Equations for Constant Acceleration

x component (horizontal)	y component (vertical)	Comments
vx = v0x + axt	vy = vy0 + ayt	same except for direction
x = x0 + vx0t + (1/2)axt2	y = y0 + vy0t + (1/2)ayt2	same except for direction
v2x = v2x0 + 2ax(x - x0)	v2y = v2y0 + 2ay(y - y0)	same except for direction

 

 

Projectile Motion

Kinematic Equations for Projectile Motion

Note that these equations are specific cases of the general equations with stated assumptions

 

Assuming y is positive upwards, a_x = 0, a_y = -g

 

Horizontal Motion: ax = 0, vx = constant	Vertical Motion: ay = -g	Comments
vx = vx0	vy = vyo - gt	ax = 0, ay ≠ 0
x = x0 + vx0t vx = vx0 (same as 1st one-reason not listed in text)	y = y0 + vy0t - (1/2)gt2 v2y = v2y0 - 2g(y - y0)	ax = 0, ay ≠ 0, ay = -g ax = 0, square root of both sides

 

Comparison of Equations for Constant Acceleration: Constant a, Constant a, x₀ = 0, q₀ = 0

Angular	Linear
w = w0 + at	v = v0 + at
q =  w0 t + (1/2)a t2	x = v0t + (1/2)at2
w2 = w02  + 2aq	v2 = v02 + 2ax
wavg= (w +w0)/2	vavg = (v + v0)/s