# An object has a mass of #4 kg#. The object's kinetic energy uniformly changes from #144 KJ# to # 120KJ# over #t in [0, 6 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 need to determine the total distance traveled by the object over the given time interval. We can then divide this distance by the total time to calculate the average speed.

First, let's find the initial and final velocities of the object using the kinetic energy:

Given: Initial kinetic energy (KE1) = 144 kJ Final kinetic energy (KE2) = 120 kJ Time interval (t) = 6 s

The change in kinetic energy (ΔKE) is given by: ΔKE = KE2 - KE1 ΔKE = 120 kJ - 144 kJ ΔKE = -24 kJ

We know that kinetic energy is given by the formula: KE = 1/2 * m * v^2

Where: KE is the kinetic energy, m is the mass of the object, and v is the velocity of the object.

Rearranging the formula to solve for velocity, we get: v = sqrt(2 * KE / m)

Using this formula, we can find the initial and final velocities of the object.

Initial velocity (v1) = sqrt(2 * KE1 / m) Final velocity (v2) = sqrt(2 * KE2 / m)

Now, let's calculate the initial and final velocities:

Initial velocity (v1) = sqrt(2 * 144 kJ / 4 kg) ≈ 12 m/s Final velocity (v2) = sqrt(2 * 120 kJ / 4 kg) ≈ 10 m/s

The average speed of the object is given by the total distance traveled divided by the total time taken.

Average speed = Total distance / Total time

Since the object's acceleration is uniform, the average speed is the arithmetic mean of the initial and final velocities:

Average speed = (Initial velocity + Final velocity) / 2

Substituting the values we found:

Average speed = (12 m/s + 10 m/s) / 2 Average speed ≈ 11 m/s

Therefore, the average speed of the object is approximately 11 meters per 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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