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The case
of constant acceleration and motion in a straight line yields some simple
equations that permit the evaluation of the velocity and position of the vehicle
if the initial conditions are known.
From the definition (dv/dt) = a, the velocity
at a later time t can be determined from the initial velocity, v(0), and the
constant acceleration, a, by integration. This gives: v(t) = v(0) + at.
From
the definitions: v
= (ds/dt)
and a
= (dv/dt)
it is seen that dt = (ds/v) = (dv/a) so that v dv= a ds. Integrating this expression
for motion between locations s = 0 and s gives: v(t)2 = v(0)2
+ 2as.
Substituting
the expression for v(t) into the definition of
velocity and integrating relates the position at any time, t, to the initial
velocity, v(0), and the constant acceleration, a: s(t) = v(0)t + at2/2. |
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