Question

A graph titled Position versus time for with horizontal axis time (seconds) and vertical axis position (meters). A straight blue line runs with an upward slope from 0 seconds 3 meters to 4 seconds 15 meters.
The starting position of this object is
m.

The object is traveling at a velocity of
m/s

Answer 1

Answer:

How are position vs. time graphs useful?

Many people feel about graphs the same way they do about going to the dentist: a vague sense of anxiety and a strong desire for the experience to be over with as quickly as possible. But position graphs can be beautiful, and they are an efficient way of visually representing a vast amount of information about the motion of an object in a conveniently small space.

What does the vertical axis represent on a position graph?

The vertical axis represents the position of the object. For example, if you read the value of the graph below at a particular time you will get the position of the object in meters.

Try sliding the dot horizontally on the graph below to choose different times and see how the position changes.

 

 

 

 

Concept check: What is the position of the object at time t=5t=5t, equals, 5 seconds according to the graph above?

[Show me the answer.]

What does the slope represent on a position graph?

The slope of a position graph represents the velocity of the object. So the value of the slope at a particular time represents the velocity of the object at that instant.

Answer 2

The starting position of the object will be 3 m and the velocity of the object will be 3 m/s

Given:

At Starting:

Position of object = 3 m

Time is taken by the object = 0 s

At Ending:

Position of object = 15 m

Time is taken by the object = 4 s

To Find:

The starting position and velocity of the object

Solution:

We can find the starting position and velocity of the object very easily as given below.

It is already given that,

When the time is equal to 0, the position of the object is at 3m

Hence, the starting position of the object will be 3 m.

We know that,

Velocity = $\frac{Change in position (d)}{Change in time (t)}$

Velocity = $\frac{\delta d }{\delta t}$

= $\frac{d2 - d1}{t2 - t1}$

We have,

d1 = 3 m

d2 = 15 m

t1 = 0 s

t2 = 4 s

By substituting the values,

Velocity = $\frac{d2 - d1}{t2 - t1}$

= $\frac{15 - 3}{4 - 0}$

= $\frac{12}{4}$

= 3 m/s

Hence, the velocity of the object is 3 m/s and the starting position of the object is 3 m

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