# An object has a mass of #9 kg#. The object's kinetic energy uniformly changes from #54 KJ# to # 0 KJ# over #t in [0, 4 s]#. What is the average speed of the object?

The average speed is

The kinetic energy is

Therefore,

and,

The equation of the line is

So,

So,

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To find the average speed of the object, we first need to calculate the change in kinetic energy and then use it to find the change in velocity. From there, we can determine the average speed by dividing the total distance traveled by the total time taken.

Given that the object's kinetic energy changes from 54 kJ to 0 kJ over a time interval of 4 seconds, we can calculate the change in kinetic energy:

Change in kinetic energy = Final kinetic energy - Initial kinetic energy = 0 kJ - 54 kJ = -54 kJ

Next, we'll use the equation for kinetic energy:

Kinetic energy = 0.5 * mass * velocity^2

We can rearrange this equation to solve for velocity:

Velocity = sqrt(2 * kinetic energy / mass)

Using this equation, we can find the initial velocity:

Initial velocity = sqrt(2 * 54 kJ / 9 kg) ≈ 6 m/s

Final velocity, since kinetic energy becomes 0 kJ, will be 0 m/s.

Now, we can calculate the average speed using the formula:

Average speed = total distance traveled / total time taken

Since the acceleration is uniform, we can use the formula for average speed:

Average speed = (initial velocity + final velocity) / 2

Plugging in the initial and final velocities:

Average speed = (6 m/s + 0 m/s) / 2 = 3 m/s

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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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