# An object has a mass of #4 kg#. The object's kinetic energy uniformly changes from #64 KJ# to # 160 KJ# over #t in [0, 12 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 use the formula:

Average speed = Total distance traveled / Total time taken

In this case, since the object's mass is given, we'll use the change in kinetic energy to calculate the total distance traveled. We'll also use the given time interval.

First, we find the change in kinetic energy: Change in kinetic energy = Final kinetic energy - Initial kinetic energy Change in kinetic energy = 160 kJ - 64 kJ = 96 kJ

Next, we convert the change in kinetic energy from kilojoules to joules: Change in kinetic energy = 96 kJ * 1000 = 96000 J

Since kinetic energy is given by the formula KE = (1/2) * m * v^2, where m is mass and v is velocity, we can rearrange the formula to solve for velocity: v = sqrt((2 * KE) / m)

Now, we plug in the values: v = sqrt((2 * 96000 J) / 4 kg)

v = sqrt(48000) m/s

v ≈ 219.088 m/s

Therefore, the average speed of the object is approximately 219.088 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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