R
ECTILINEAR
M
OTION
Velocity and Acceleration
•
Calculus is most useful when we apply meanings of the derivative other than just the
slope of a tangent to a curve.
•
If we have an object moving along a straight line we call this motion rectilinear
motion.
To model this, we consider a horizontal line with distances to right of the
origin as positive and distances to the left of the origin as negative.
0

ç
=====
====
è
+
•
Let
f
be a function that relates the distance
s
from 0 and time
t
, and then we can write
)
(
t
f
s
=
, where
s
(displacement) could be the number of meters travelled from 0 in
t
seconds.
ime
change
ce
s
changeindi
velocity
int
tan
=
Eg.
If you drive 30 km in 20 min, your velocity over the 30km is
h
km
hr
km
km
/
90
3
/
1
30
min
20
30
=
=
Of course, this is average velocity, you probably weren’t going 90km/h the whole time.
We are more interested in instantaneous velocity
.
So, to define the velocity of an object at a time
0
t
to
t
t
∆
+
0
and let
0
→
∆
t
.
Then if the
distance travelled by time
0
t
is
)
(
0
t
f
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 Fall '08
 Kim
 Calculus, Derivative, Slope, Velocity

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