a. On what intervals is the object moving in the positive direction? Consider the graph shown in the figure, which gives the velocity of an object moving along a line. Assume time is measured in hours and distance is measured in miles. The areas of three regions bounded by the velocity curve and the t-axis are also given. Complete parts (a) through (e). The object is moving in the positive direction when its velocity is positive. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. V A. The object is moving in the positive direction on the interval(s) [0,1).(3,5). (Type your answer in interval notation. Use a comma to separate answers as needed.) 12 11 4 OB. The object is never moving in the positive direction. 15 b. Use the values shown in the graph to set up an expression that gives the displacement of the object over the interval [0,3]. Ignoring units, the expression of the object over [0,3]. (Do not perform the calculation.) gives the displacement
Optimization
Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.
Integration
Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.
Application of Integration
In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.
Volume
In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).
Area
Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.
![a. On what intervals is the object moving in the positive
direction?
Consider the graph shown in the figure, which gives the
velocity of an object moving along a line. Assume time is
measured in hours and distance is measured in miles.
The areas of three regions bounded by the velocity curve
and the t-axis are also given. Complete parts (a) through
(e).
The object is moving in the positive direction when its
velocity is positive.
Select the correct choice below and, if necessary, fill in
the answer box to complete your choice.
A. The object is moving in the positive direction on
the interval(s) [0,1),(3,5).
(Type your answer in interval notation. Use a
comma to separate answers as needed.)
12
11
1
OB. The object is never moving in the positive
direction.
4
15
b. Use the values shown in the graph to set up an
expression that gives the displacement of the object over
the interval [0,3].
Ignoring units, the expression
of the object over [0,3].
(Do not perform the calculation.)
gives the displacement](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff3c0899a-5c62-4a86-a39c-5b160af6a916%2F83afd896-6013-45ca-b437-37d5c17b0d0a%2Fwibk6z_processed.jpeg&w=3840&q=75)
Given the velocity-time graph or v-t graph.
The area under the graph gives the distance.
We need to find the expression for diaplacement from t = 0 to t=3.
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