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CBR
35
Teacher information
(cont.)
The mathematics of distance, velocity, and acceleration
Distance-Time plot
V
average
=
@
d
@
t
=
d
2
N
d
1
t
2
N
t
1
= slope of Distance-Time plot
V
instantaneous
=
lim
@
t
"
0
(
@
d
@
t
)
=
d(s)
dt
where
s
= distance
Velocity-Time plot
A
average
=
@
v
@
t
=
v
2
N
v
1
t
2
N
t
1
= slope of Velocity-Time plot
A
instantaneous
=
lim
@
t
"
0
(
@
v
@
t
)
=
dv
dt
The area under the Velocity-Time plot from
t
1
to
t
2
= @
d
= (
d
2
N
d
1
) = displacement from
t
1
to
t
2
(net distance traveled).
So, @
d
=
(
∑
t=1
t=2
v(
@
t)
)
or @
d
=
⌡
⌠
t=1
t=2
v(dt)
Acceleration-Time plot
t
1
t
2
t
1
t
2
t
1
t
2
v
1
v
2
d
2
d
1
@
t