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Motion with Constant Velocity
Now that we have an idea of position and average velocity, we’ll look at how the position of an object
is effected when it moves with constant velocity.
First of all, note that constant velocity entails an object moving in the same direction at the same speed
for the duration of the problem, or at least the part of the problem that we’re interested in examining.
Next, note that if something moves at a constant velocity (which means that the velocity doesn’t change
as time progresses) then that velocity will be the average velocity, or v = vavg .
Now, I’ll introduce some notation that will be standard throughout the course. When the initial position
corresponds to t = 0 then we refer to that initial position as x0 . This is true for intial velocity or anything
else, as long as the problem starts at t = 0. We’ll be able to do this with all the problems we see. Note that
∆t = tf − ti = tf − 0 = tf when this is the case.
x −x
From the definition of average velocity, we can take v = ftf 0 . Rearranging the terms, we get xf =
vtf + x0 . Noting that this is valid for any tf , we can just replace this parameter with t to get a continuous
function of position with time.
Position as a function of time with constant velocity
x(t) = vt + x0
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