# Displacement, velocity and acceleration

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• May 25th 2010, 06:48 AM
lorica2000
Displacement, velocity and acceleration
The formula for distance, velocity and acceleration are derived in calculus using s = Svdt(S-integral) and v = at +v0
derive the formula for distance(s) using velocity and the initial velocity v0
• May 25th 2010, 08:03 AM
skeeter
Quote:

Originally Posted by lorica2000
The formula for distance, velocity and acceleration are derived in calculus using s = Svdt(S-integral) and v = at +v0
derive the formula for distance(s) using velocity and the initial velocity v0

assuming acceleration is constant ...

$
v = v_0 + at
$

$
\frac{ds}{dt} = v_0 + at
$

$
ds = (v_0 + at) \, dt
$

$
\int ds = \int (v_0 + at) \, dt
$

$
s = s_0 + v_0 t + \frac{1}{2}at^2
$