# Find the object’s speeds v1. v2. and v3 at times t1=2.0s. t2=4.0s. and t3=13s.

Find the object’s speeds v1, v2, and v3 at times t1=2.0s,
two significant figures, separated by commas. Tactics Box 2.1 Interpreting Position-versus-Time Graphs Learning Goal To practice Tactics Box 2.1 Interpreting position-versus-time graphs. A continuous curve that shows an object’s position as a function of time is called a position-versus-time graph. You can gain relevant information on an object’s motion if you interpret such graphs correctly. To do that, it is useful to review the definition of velocity. For motion along a line, the velocity vz is the ratio of the displacement Δπ of an object to the time interval Δt during which this displacement occurs, which can be written as Part B Find the object’s speeds u1 , U2, and U3 at times t1 = 2.0 s, t2 = 4.0 s, and t3 = 13 s. Express your answers in meters per second to two significant figures, separated by commas Figure 1 of 1 2.3,0,-0.75 m/s, m/s, m/s v1 , v2 , v3= V1, U2, U3 x (m) Submit My Answers Give Up 12 10 Incorrect; Try Again; 2 attempts remaining 4 0 2 4 6 8 10 12 14 16

General guidance

Concepts and reason
This problem uses the concept of equation of slope of a line.
Use the concept of equation of slope of a line to find the velocity at different times.

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Fundamentals

The Equation for the slope of line is as follows:

Here, is the slope of line, is one point on y axis, is the point on x axis, is the other point of y axis, and is the point x axis.

Step-by-step

Step 1 of 3

(B.1)
The Equation for the slope of line is as follows:

Substitute for , for , for , and for in.

The slope of line is equal to the velocity of an object.
Therefore,
…… (1)
Here, velocity is .
Substitute for .

Part B.1
Velocity of an object at time is .

The velocity of the object varies uniformly as seen from graph. The velocity of the object is basically the slope of line from the graph that starts from origin, that is and ends at . The slope of line is basically the ratio of change in coordinates and change in x coordinates.

The incorrect Equation for the slope of line is because the correct expression is .

Use the expression to calculate velocity of an object at .

Step 2 of 3

(B.2)
The Equation for the slope of line is as follows:

Substitute for , for , for , and for .

Substitute for in equation (1).

Part B.2
The velocity of an object at is .

Here, from the graph the slope remains zero throughout the points and .
The point lies between these two points. The displacement is zero of the object during this time interval. As displacement is zero throughout the interval. Thus, velocity is zero.

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Take the slope carefully.

Use the expression to calculate velocity of an object at .

Step 3 of 3

(B.3)
The Equation for the slope of line is as follows:

Substitute for , for , for , and for .

Substitute for in Equation (1).

Part B.3
The velocity of an object at is .

Calculate the slope of line from point and . On this line lies the time . During this time, the velocity remains constant because the slope between these two points is constant.

Do not take that the slope of the line is not equal to the velocity.

Part B.1
Velocity of an object at time is .

Part B.2
The velocity of an object at is .

Part B.3
The velocity of an object at is .

Part B.1
Velocity of an object at time is .

Part B.2
The velocity of an object at is .

Part B.3
The velocity of an object at is .

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