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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).

asked Mar 29, 2015 in PRECALCULUS by anonymous

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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

answered Mar 29, 2015 by bradely Mentor
edited Mar 30, 2015 by bradely

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.

answered Mar 30, 2015 by yamin_math Mentor
edited Mar 30, 2015 by yamin_math

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.

answered Mar 30, 2015 by yamin_math Mentor
edited Mar 30, 2015 by yamin_math

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.

answered Mar 30, 2015 by yamin_math Mentor
edited Mar 30, 2015 by yamin_math

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.

answered Mar 30, 2015 by yamin_math Mentor
edited Mar 30, 2015 by yamin_math

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.

answered Mar 30, 2015 by cameron Mentor

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