# The displacement (in meters) of a particle moving in a straight line is given by s = 2 t^3 where t is measured in seconds. How do you find the average velocity of the particle over the time interval [ 5 , 7]?

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To find the average velocity of the particle over the time interval [5, 7], you need to calculate the change in displacement (Δs) divided by the change in time (Δt) over that interval.

First, find the displacement at time t = 5 seconds: s(5) = 2(5)^3 = 250 meters

Next, find the displacement at time t = 7 seconds: s(7) = 2(7)^3 = 686 meters

Then, calculate the change in displacement: Δs = s(7) - s(5) = 686 - 250 = 436 meters

Finally, calculate the change in time: Δt = 7 - 5 = 2 seconds

Now, find the average velocity using the formula: Average velocity = Δs / Δt

Average velocity = 436 meters / 2 seconds = 218 meters/second

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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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