# An object has a mass of #6 kg#. The object's kinetic energy uniformly changes from #18 KJ# to # 4KJ# over #t in [0,12s]#. What is the average speed of the object?

9.47 m/s

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To find the average speed of the object, we first need to calculate the initial and final velocities of the object using the given kinetic energy values.

Given: Initial kinetic energy (KE_initial) = 18 kJ Final kinetic energy (KE_final) = 4 kJ Time interval (t) = 12 s Mass of the object (m) = 6 kg

Using the formula for kinetic energy:

KE = (1/2) * mass * velocity^2

We can rearrange the formula to solve for velocity:

velocity = sqrt((2 * KE) / mass)

Substituting the given values, we find the initial and final velocities:

Initial velocity (v_initial) = sqrt((2 * 18 kJ) / 6 kg) Final velocity (v_final) = sqrt((2 * 4 kJ) / 6 kg)

Once we have the initial and final velocities, we can find the average speed using the formula:

Average speed = Total distance traveled / Total time taken

Since the object's motion is uniformly changing, we can use the average of the initial and final velocities as the object's constant velocity during the time interval.

Average speed = (v_initial + v_final) / 2

Calculate the initial and final velocities using the given kinetic energy values and mass.

Then, find the average speed using the formula mentioned above.

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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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