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It is my understanding that to calculate the change of kinetic energy of an object that speeds up from v

Change of kinetic energy = 1/2 * m * (v

When the initial velocity is 0 m/s I have no problems, but let's say an object that weighs 2 kg speeds up from 20 m/s to 40 m/s.

When I use the formula I mentioned, I get:

ΔE

Now let's say the initial velocity is 0 m/s, final 20 m/s. I then get:

ΔE

Does this make sense? The same changes in velocity and different changes in kinetic energy?

Should I not use a formula like this instead:

ΔE

?

Then I end up with 400 J in both cases.

Also, what if the initial velocity is, lets's say 5 m/s and final -5 m/s? Does the kinetic energy change?

_{i}to v_{f}you use this formula:Change of kinetic energy = 1/2 * m * (v

_{f}^{2}- v_{i}^{2})When the initial velocity is 0 m/s I have no problems, but let's say an object that weighs 2 kg speeds up from 20 m/s to 40 m/s.

When I use the formula I mentioned, I get:

ΔE

_{k}= 1/2 * 2 * (1600 - 400) = 1200 JNow let's say the initial velocity is 0 m/s, final 20 m/s. I then get:

ΔE

_{k}= 1/2 * 2 * (400 - 0) = 400 JDoes this make sense? The same changes in velocity and different changes in kinetic energy?

Should I not use a formula like this instead:

ΔE

_{k}= 1/2 * m * (Δv)^{2}= 1/2 * m * (v_{f}- v_{i})^{2}?

Then I end up with 400 J in both cases.

Also, what if the initial velocity is, lets's say 5 m/s and final -5 m/s? Does the kinetic energy change?

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