Nonuniform straight-line motion Consider the motion of an object given by the position function r ( t ) = f ( t ) 〈 a , b , c 〉 + 〈 x 0 , y 0 , z 0 〉 , for t ≥ 0 , where a, b, c , x 0 , y 0 , and z 0 are constants, and f is a differentiable scalar function, for t ≥ 0. a. Explain why this function describes motion along a line. b. Find the velocity function. In general, is the velocity constant in magnitude or direction along the path?
Nonuniform straight-line motion Consider the motion of an object given by the position function r ( t ) = f ( t ) 〈 a , b , c 〉 + 〈 x 0 , y 0 , z 0 〉 , for t ≥ 0 , where a, b, c , x 0 , y 0 , and z 0 are constants, and f is a differentiable scalar function, for t ≥ 0. a. Explain why this function describes motion along a line. b. Find the velocity function. In general, is the velocity constant in magnitude or direction along the path?
Solution Summary: The author explains why the function describes motion along a line.
Nonuniform straight-line motion Consider the motion of an object given by the position function
r
(
t
)
=
f
(
t
)
〈
a
,
b
,
c
〉
+
〈
x
0
,
y
0
,
z
0
〉
,
for
t
≥
0
,
where a, b, c, x0, y0, and z0 are constants, and f is a differentiable scalar function, for t ≥ 0.
a. Explain why this function describes motion along a line.
b. Find the velocity function. In general, is the velocity constant in magnitude or direction along the path?
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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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