383
Answers
601–700
Answers and Explanations
Therefore, the velocity function is
v t
t t
( ) = + −
2
12
Next, find the displacement by integrating the velocity function over the given interval,
0 ≤ t ≤ 5:
s
s
t t
dt
t
t
t
( ) ( )
( )
5
0
12
3 2
12
5
3
5
2
12 5
2
0
5
3
2
0
5
3
2
−
=
+ −
(
)
=
+ −






=
+
−
∫
− − + −
(
)
= −
0 0 0
35
6
632.
3
3
2
+
First find the velocity function by evaluating the antiderivative of the acceleration
function, a
 
(t) = sin t + cos t:
v t
t
t dt
t
t C
( )
(sin cos )
cos sin
=
+
= −
+
+
∫
Next, use the initial condition, v π
4
0
( ) = , to solve for the arbitrary constant of
integration:
C
v
C
C
C
π
π
π
π
π
4
4
4
0
4
4
0
2
2
2
2
0
( ) = − + +
= −
+
+
= −
+
+
=
cos
sin
cos
sin
Therefore, the velocity function is
v t
t
t
( )
cos sin
= −
+
Next, find the displacement by integrating the velocity function over the given interval,
π
π
6
≤ ≤
t
:
s
s
t
t dt
t
t
π
π
π
π
π
π
π
π
( )− ( ) = − +
(
)
= −
−
(
)
= −
−
− −
∫
6
6
6
cos sin
sin cos
sin
cos
s sin
cos
π
π
6
6
0 1
1
2
3
2
3
3
2
−
(
)
= − + − − −






= +