# How do you find the average velocity of the position function #s(t)=3t^2-6t# on the interval from #t=2# to #t=5#?

Average velocity is defined as total displacement/ total time taken for that

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To find the average velocity of the position function ( s(t) = 3t^2 - 6t ) on the interval from ( t = 2 ) to ( t = 5 ), you can use the formula:

[ \text{Average velocity} = \frac{\text{Change in position}}{\text{Change in time}} ]

The change in position is found by evaluating ( s(5) - s(2) ), and the change in time is ( 5 - 2 ).

So, the average velocity is:

[ \text{Average velocity} = \frac{s(5) - s(2)}{5 - 2} ]

[ \text{Average velocity} = \frac{(3(5)^2 - 6(5)) - (3(2)^2 - 6(2))}{5 - 2} ]

[ \text{Average velocity} = \frac{(75 - 30) - (12 - 12)}{3} ]

[ \text{Average velocity} = \frac{45}{3} ]

[ \text{Average velocity} = 15 ]

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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