# The kinetic energy of an object with a mass of #3 kg# constantly changes from #60 J# to #270 J# over #8 s#. What is the impulse on the object at #5 s#?

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Unanswerable

Impulse is defined as the force exerted over a time interval. Asking what the impulse is at a specific instant of time makes no sense. Impulse is equivalent to the total change in momentum. It is often useful when we know an initial and final velocity, but we don't know if the change was made because of a small force acting over a long time, or a large force acting very quickly.

A question concerning the total impulse exerted over the first five seconds could be asked, as well as questions concerning the force, acceleration, and velocity at a specific moment in time. If you were attempting to answer one of those questions, please submit a different one.

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To find the impulse at 5 seconds, we first need to determine the initial and final velocities of the object at that time. We can use the formula for kinetic energy to find the initial and final velocities:

Initial kinetic energy = 60 J Final kinetic energy = 270 J Mass = 3 kg

Using the formula for kinetic energy:

(KE = \frac{1}{2}mv^2)

(60 = \frac{1}{2}(3)v^2) (v_{initial} = \sqrt{\frac{60 \times 2}{3}})

(v_{initial} ≈ 7.75 m/s)

(270 = \frac{1}{2}(3)v^2) (v_{final} = \sqrt{\frac{270 \times 2}{3}})

(v_{final} ≈ 17.32 m/s)

Now, we can use the definition of impulse:

(Impulse = m \cdot \Delta v)

(Impulse = 3 \cdot (17.32 - 7.75))

(Impulse ≈ 28.17 , N \cdot 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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