Formulas & tables/Physics/Kinematics/Distance in uniformly accelerated motion

Distance in uniformly accelerated motion

s=v_0 t+\tfrac12 a t^2

Result unit: m (metre)

What it describes

Distance in uniformly accelerated motion — the sum of the distance due to the initial velocity and the extra distance due to the acceleration.

s

distance

[m]

v_0

initial velocity

[m/s]

t

time

[s]

a

acceleration

[m/s²]

The distance has two parts: the distance the body would cover at its initial velocity (

v_0 t

), plus the extra distance due to the acceleration (

\tfrac12 a t^2

Uniformly accelerated or decelerated motion (then

a<0

). Starting from rest

v_0=0

and the formula simplifies to

s=\tfrac12 a t^2

A body starts with

v_0=2

m/s and accelerates at

a=3

m/s² for 4 s. Find the distance.

Substitution

v_0=2

a=3

t=4

Result

s=2\cdot4+\tfrac12\cdot3\cdot4^2=8+24=32

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