Displacement, distance, and position Consider an object moving along a line with the following velocities and initial positions. Assume time t is measured in seconds and velocities have units of m/s. a. Over the given interval, determine when the object is moving in the positive direction and when it is moving in the negative direction. b. Find the displacement over the given interval. c. Find the distance traveled over the given interval. d. Determine the position function s ( t ) using the Fundamental Theorem of Calculus ( Theorem 6.1 ). Check your answer by finding the position function using the antiderivative method. 3. v ( t ) = 12 t 2 − 30 t + 12 , for 0 ≤ t ≤ 3 ; s ( 0 ) = 1
Displacement, distance, and position Consider an object moving along a line with the following velocities and initial positions. Assume time t is measured in seconds and velocities have units of m/s. a. Over the given interval, determine when the object is moving in the positive direction and when it is moving in the negative direction. b. Find the displacement over the given interval. c. Find the distance traveled over the given interval. d. Determine the position function s ( t ) using the Fundamental Theorem of Calculus ( Theorem 6.1 ). Check your answer by finding the position function using the antiderivative method. 3. v ( t ) = 12 t 2 − 30 t + 12 , for 0 ≤ t ≤ 3 ; s ( 0 ) = 1
Displacement, distance, and position Consider an object moving along a line with the following velocities and initial positions. Assume time t is measured in seconds and velocities have units of m/s.
a. Over the given interval, determine when the object is moving in the positive direction and when it is moving in the negative direction.
b. Find the displacement over the given interval.
c. Find the distance traveled over the given interval.
d. Determine the position function s(t) using the Fundamental Theorem of Calculus (Theorem 6.1). Check your answer by finding the position function using the antiderivative method.
3.
v
(
t
)
=
12
t
2
−
30
t
+
12
, for
0
≤
t
≤
3
;
s
(
0
)
=
1
Let f be a function whose graph consists of 5 line segments and a semicircle as shown in the figure below.
Let g(x) = √ƒƒ(t) dt .
0
3
2
-2
2
4
5
6
7
8
9
10
11
12
13
14
15
1. g(0) =
2. g(2) =
3. g(4) =
4. g(6) =
5. g'(3) =
6. g'(13)=
The expression 3 | (3+1/+1)
of the following integrals?
A
Ов
E
+
+
+ +
18
3+1+1
3++1
3++1
(A) √2×14 dx
x+1
(C) 1½-½√ √ ² ( 14 ) d x
(B) √31dx
(D) So 3+x
-dx
is a Riemann sum approximation of which
5
(E) 1½√√3dx
2x+1
2. Suppose the population of Wakanda t years after 2000 is given by the equation
f(t) = 45000(1.006). If this trend continues, in what year will the population reach 50,000
people? Show all your work, round your answer to two decimal places, and include units. (4
points)
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