# An object has a mass of #4 kg#. The object's kinetic energy uniformly changes from #12 KJ# to # 72KJ# over #t in [0,5s]#. What is the average speed of the object?

133.63 m/s

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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:

First, calculate the change in kinetic energy: ΔKE = Final KE - Initial KE ΔKE = 72 kJ - 12 kJ = 60 kJ

Next, use the formula for kinetic energy: KE = 0.5 * mass * velocity^2

Rearrange the formula to solve for velocity: velocity = √(2 * KE / mass)

Substitute the values and solve for velocity: velocity = √(2 * 60 kJ / 4 kg) ≈ √30 m/s

Finally, calculate the average speed: Average speed = Total distance / Total time Since the object's speed changes uniformly, its average speed is half of its final velocity.

Average speed ≈ 0.5 * √30 m/s ≈ 2.74 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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