Version One – Homework 2 – Heinz – 81204 – Sep 02, 2004
2
an initial position of

30 m and an initial
velocity of 4 m
/
s.

4

3

2

1
0
1
2
3
4
5
6
0
1
2
3
4
5
6
7
8
9
time (s)
acceleration (m/s
2
)
What is the velocity at 3 s?
Correct answer:

5 m
/
s.
Explanation:
In order to use the above graph, let
x
0
=
x
0
,
1
=

30 m
,
v
0
=
v
0
,
1
= 4 m
/
s
,
(
t
0
, a
0
) = (
t
0
,
1
, a
0
) = (0 s
,
0 m
/
s
2
)
,
(
t
1
, a
1
) = (
t
0
,
1
, a
1
,
2
) = (0 s
,

3 m
/
s
2
)
,
(
t
2
, a
2
) = (
t
2
,
3
, a
1
,
2
) = (4 s
,

3 m
/
s
2
)
,
(
t
3
, a
3
) = (
t
2
,
3
, a
3
,
4
) = (4 s
,
5 m
/
s
2
)
,
(
t
4
, a
4
) = (
t
4
,
5
, a
3
,
4
) = (9 s
,
5 m
/
s
2
)
,
and
(
t
5
, a
5
) = (
t
4
,
5
, a
5
) = (9 s
,
0 m
/
s
2
)
.
Basic Concepts:
The plot shows a curve
of
acceleration
versus
time
.
The change in velocity is the area (
a
1
,
2
t
)
between the acceleration curve and the time
axis
v
=
v
0
,
1
+
a
1
,
2
t ,
where the acceleration is constant.
Solution:
With constant acceleration (
a
1
,
2
=

3 m
/
s
2
),
v
=
v
0
,
1
+
a
1
,
2
t
(1)
= (4 m
/
s) + (

3 m
/
s
2
) (3 s)
=

5 m
/
s
.
Equations 1 and 3 are plotted below.

1
0
1
2
0
1
2
3
4
5
6
7
8
9
time (s)
velocity (m/s) [
×
0
.
1]
007
(part 2 of 4) 2 points
What is the position at 3 s?
Correct answer:

31
.
5 m.
Explanation:
Basic Concepts:
The change in position
is the area (
v
0
,
1
t
+
1
2
a t
2
) between the veloc
ity curve and the time axis
x
=
x
0
,
1
+
v
0
,
1
t
+
1
2
a t
2
.
Solution:
With
constant
acceleration
(
a
1
,
2
=

3 m
/
s
2
),
x
=
x
0
,
1
+
v
0
,
1
t
+
1
2
a
1
,
2
t
2
(2)
= (

30 m) + (4 m
/
s) (3 s)
+
1
2
(

3 m
/
s
2
) (3 s)
2
=

31
.
5 m
.