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Formulas of Motion
Linear and angular acceleration, velocity and displacement
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Linear Motion Formulas
Velocity can be expressed as (velocity is constant):
v = s / t (1a)
where
v = velocity (m/s, ft/s)
s = linear displacement (m, ft)
t = time (s)
Velocity can be expressed as (acceleration is constant):
v = v0 + a t (1b)
where
v0 = initial linear velocity (m/s, ft/s)
a = acceleration (m/s2, ft/s2)
Linear displacement can be expressed as (acceleration is constant):
s = v0 t + 1/2 a t2 (1c)
Combining 1a and 1c to express the final velocity
v = (v02 + 2 a s)1/2 (1d)
Velocity can be expressed as (velocity is variable)
v = ds / dt (1f)
where
ds = change of displacement (m, ft)
dt = change in time (s)
Acceleration can be expressed as
a = dv / dt (1g)
where
dv = change in velocity (m/s, ft/s)
Angular Motion Formulas
Angular velocity can be expressed as (angular velocity = constant):
ω = θ / t (2a)
where
ω= angular velocity (rad/s)
θ = angular displacement (rad)
t = time (s)
Angular velocity can be expressed as (angular acceleration is constant):
ω = ωo + α t (2b)
where
ωo = angular velocity at time zero (rad/s)
α = angular acceleration (rad/s2)
Angular displacement can be expressed as (angular acceleration is constant):
θ = ωo t + 1/2 α t2 (2c)
Combining 2a and 2c:
ω = (ωo2 + 2 α θ)1/2
Angular acceleration can be expressed as:
α = dω / dt = d2θ / dt2 (2d)
where
dθ = change of angular displacement (rad)
dt = change in time (s)
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