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In discussing motion, there are three

closely related concepts that you needto keep straight. These are:

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1) Position: x(t)determines where theobject is on the x-axis at a given time t

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2)Velocity: v(t) = x(t)determines howfast the position is changing at time t

as well as the direction of movement

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3) Acceleration: a(t) = v(t) = x(t)determines how fast the velocity is

changing at time t; the sign indicates if

velocity is increasing or decreasing

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If x(t) represents the position of a

particle along the x-axis at any time t,

then the following statements are

true:

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1) Initially means when time t= 0

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2) At the origin means when positionx(t)= 0

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3) At rest means velocity v(t)= 0

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4) If the velocity of the particle ispositive,then the particle is moving

to the right.

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5) If the velocity of the particle isnegative, then the particle is moving

to the left.

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6) To find average velocity over a timeinterval, divide the change in

position by the change in time.

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7) Instantaneous velocity is thevelocity at a single moment (instant)

in time.

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8) If the acceleration of the particle ispositive, then the velocity is

increasing.

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9) If the acceleration of the particle isnegative, then the velocityis

decreasing.

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10) In order for a particle to changedirections, the velocitymust change

signs.

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11) One way to determine the totaldistance traveled over a time interval is

to find the sum of the absolute values

of the differences in position betweenall resting points. Heres an example: If

the position of a particle is given by:

x(t)= , find the distance traveled

on the interval .

4331 23 ttt

60 t

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11) To find when the particle changeddirections, we must first find the

times at which object stood still

which is when the velocity = 0.

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11) contdV(t) = x(t) = t2-2t-3.

t2-2t-3 = 0

(t-3)(t+1) =0

t = 3 or t = -1 (which is not in [0,6]),

so t = 3 is the only time the objectchanges directions.

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11) contd.Now, lets see where the object starts,

comes to rest and ends.

X(0) = 4 (where the object starts)

X(3) = -5(where the object comes to

rest )

X(6) = 22 (where the object ends)

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11) contd.So the object starts 4 units to the right,

moves to -5 which is 9 units to the

left, then ends at 22 which is 27 units

to the right. So the total distance

traveled is 9 + 27 = 36.

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In-class Assignment 3-4A

Pg. 129 #1-