Graphics Reference
In-Depth Information
“acc” must be equal to the area above the curve marked “dec,” but the actual values of the acceleration
and deceleration do not have to be equal to each other. Thus, three of the four variables (
acc
,
dec
,
t
1
,
t
2
)
can be specified by the user and the system can solve for the fourth to enforce the constraint of equal
areas (see
Figure 3.16
)
.
This piecewise constant acceleration function can be integrated to obtain the velocity function. The
resulting velocity function has a linear ramp for accelerating, followed by a constant velocity interval,
and ends with a linear ramp for deceleration (see
Figure 3.17
). The integration introduces a constant
into the velocity function, but this constant is 0 under the assumption that the velocity starts out at 0 and
ends at 0. The constant velocity attained during the middle interval depends on the total distance that
acc
acceleration/deceleration
0.0
t
time
dec
0.0
t
1
t
2
1.0
a
acc
0
t
t
1
a
0.0
t
1
t
t
2
a
dec
t
2
t
1.0
FIGURE 3.16
Constant acceleration/deceleration graph.
v
0
velocity
0.0
1.0
t
1
t
2
time
t
t
1
---
v
v
0
·
0.0
t
t
1
v
v
0
t
1
t
t
2
⎛
t
2
1
t
2
t
t
2
t
1.0
v
v
0
·
⎜
⎝
1.0
FIGURE 3.17
Velocity-time curve for constant acceleration. Area under the curve equals the distance traveled.
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