Suppose that its velocity function is given by #v(t) = 4t^2 -8t# where t is in seconds, how do you find the object's average acceleration along the time interval [3, 9] seconds?

Answer 1

Please see below.

The acceleration is the rate of change of velocity.

The average rate of change of a function #f# on an interval #[a,b]# is
#(f(b)-f(a))/(b-a)#

So, the average acceleration we have been asked for is

#(v(9)-v(3))/(9-3) = 40# (distance/sec/sec)
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Answer 2

To find the object's average acceleration along the time interval [3, 9] seconds, you can use the formula for average acceleration, which is the change in velocity divided by the change in time:

Average acceleration = (change in velocity) / (change in time)

To calculate the change in velocity, subtract the velocity at the initial time from the velocity at the final time:

Change in velocity = v(9) - v(3)

Substitute the given velocity function v(t) = 4t^2 - 8t into this expression and evaluate it:

v(9) = 4(9)^2 - 8(9) v(3) = 4(3)^2 - 8(3)

Then, plug these values into the formula for change in velocity and compute the result.

Finally, divide the change in velocity by the change in time (which is 9 - 3 = 6 seconds) to find the average acceleration.

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Answer from HIX Tutor

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.

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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