# An object has a mass of #12 kg#. The object's kinetic energy uniformly changes from #96 KJ# to # 160 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 using the given values:

Change in kinetic energy = Final kinetic energy - Initial kinetic energy = 160 kJ - 96 kJ = 64 kJ

Next, we use the formula for kinetic energy:

Kinetic energy = (1/2) * mass * velocity^2

Since the mass is constant, we can set up the equation:

(1/2) * mass * (final velocity^2 - initial velocity^2) = 64 kJ

Solve for final velocity:

final velocity^2 = (2 * 64 kJ) / mass + initial velocity^2

Substitute the given values and solve for final velocity:

final velocity^2 = (2 * 64 kJ) / 12 kg + 0 m/s^2 final velocity^2 = (128 kJ) / 12 kg final velocity^2 = 10.67 m^2/s^2

Take the square root of both sides to find the final velocity:

final velocity ≈ √10.67 m/s final velocity ≈ 3.27 m/s

Now, we can find the average speed of the object using the formula:

Average speed = Total distance / Total time

Since the object's motion is uniformly accelerated, the average speed is equal to the average velocity, which is half the sum of the initial and final velocities:

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

Substitute the given values and solve:

Average speed = (0 m/s + 3.27 m/s) / 2 Average speed ≈ 1.64 m/s

Therefore, the average speed of the object is approximately 1.64 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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