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Algebra
Pregunta

6.The position of an object is given by $$\displaystyle s\left( t \right) = {\cos ^2}\left( {\frac{{3t - 6}}{2}} \right)$$ answer each of the following questions.

Compute (accurate to at least 8 decimal places) the average velocity of the object between $$t = 2$$ and the following values of $$t$$. Make sure your calculator is set to radians for the computations.

2.5

2.1

2.01

2.001

2.0001

1.5

1.9

1.99

1.999

1.9999

Use the information from (a) to estimate the instantaneous velocity of the object at $$t = 2$$ and determine if the object is moving to the right (i.e. the instantaneous velocity is positive), moving to the left (i.e. the instantaneous velocity is negative), or not moving (i.e. the instantaneous velocity is zero).

$A.V. = \frac{{s\left( t \right) - s\left( 2 \right)}}{{t - 2}} = \frac{{{{\cos }^2}\left( {\frac{{3t - 6}}{2}} \right) - 1}}{{t - 2}}$
Now, all we need to do is construct a table of the value of $${m_{PQ}}$$ for the given values of $$x$$. All of the values in the table below are accurate to 8 decimal places.
From the table of values above we can see that the average velocity of the object is moving towards a value of 0 from both sides of $$t = 2$$ and so we can estimate that the instantaneous velocity is 0 and so the object will not be moving at $$t = 2$$.