help please.

Question

4)  Use the information from #3 to estimate the instantaneous velocity of the object at t = 5 and determine if the object is moving left (negative), right (positive) or not moving (zero).

Answer 1

Position of the object,s = t^2 +(72/t+1)

a)

Find the position at t = 5 sec

s1 = s| t = 5 sec

    =  5^2 +(72/ (5+1))

    =25+12

     =37

Find the position at t = 5.5 sec

s2 = s| t = 5.5 sec

    =  5.5^2 +(72/ (5.5+1))

      =41.33

Find average velocity:

v avg  =(s2 - s1) / (t2 - t1)

          = (41.33 - 37)/(5.5 - 5)

          = 8.654

 

Answer 2

1(b)

Step 1 :

The position of an object is .

The average velocity of an object :

The average velocity of an object between and .

Solution :

The average velocity of an object between and is 8.1327869.

Answer 3

1(c)

Step 1 :

The position of an object is .

The average velocity of an object :

The average velocity of an object between and .

Solution :

The average velocity of an object between and is 8.01332779.

Answer 4

1(d)

Step 1 :

The position of an object is .

The average velocity of an object :

The average velocity of an object between and .

Solution :

The average velocity of an object between and is 8.0013333.

Answer 5

1(e)

Step 1 :

The position of an object is .

The average velocity of an object :

The average velocity of an object between and .

Solution :

The average velocity of an object between and is 7.318181818.

Answer 6

1(f)

Step 1 :

The position of an object is .

The average velocity of an object :

The average velocity of an object between and .

Solution :

The average velocity of an object between and is 7.86610169.

Answer 7

1(g)

Step 1 :

The position of an object is .

The average velocity of an object :

The average velocity of an object between and .

Solution :

The average velocity of an object between and is 7.986661.

Answer 8

1(h)

Step 1 :

The position of an object is .

The average velocity of an object :

The average velocity of an object between and .

Solution :

The average velocity of an object between and is 7.9986666.

Answer 9

Step 1 :

The position of an object is .

Instantaneous velocity of an object at is defined as .

Consider .

Differentiate on each side with respect to .

Substitute in above expression to find instantaneous velocity.

Instantaneous velocity of an object at is 8.

Since the result is positive , then it is to be said that the object is moving right side.

Solution :

Instantaneous velocity of an object at is 8.

Object is moving right side.