Prince Vegeta from the fallen Saiyan race is fighting against Goku.
If Vegeta attacks Goku from 13 metres away with a flying kick using 0.615384615J of Kinetic Energy in just three seconds, then punches him from only a metre away with his (metric) ton fist moving at 3.1591138m/s in another three seconds and then transfers 130000.5J of energy into going Super Saiyan in the next nine seconds: are his power levels truly over 9000?
(Thanks to Dragonlucky86 from Deviant Art for the graphic!)
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To find out if Vegeta's power levels are truly over 9000 we need to find out his actual power level.
The equation for power is work done divided by time taken, so we need to find out both of those values.
Let's start with the easy one; time taken.
The kick takes 3 seconds, the punch takes 3 seconds and the Super Saiyan-ing takes 9 seconds leaving us with a total of 3+3+9=15 seconds time taken.
Now the work done.
The flying kick uses 0.615384615J of Kinetic Energy at a distance of 13 metres. Work Done = force x distance moved, so 0.615385615 x 13 = 8.000012995J The punch is a little different because we are not given the energy but the weight of his fist, the speed of the punch and the distance but from this we can calculate the work done.
Kinetic Energy = 1/2 x mass x velocity^2 so 0.5 x 1000kg (1 metric ton) x 3.1591138^2 = 4990.000001J And now back to our Work Done equation; the distance was one metre so the energy and work done are both 4990.000001J
We are given the amount of energy transferred for the Super Saiyan-ing: 130000.5J so we do not need to calculate that.
Now to add up the total work done ~ 130000.5 + 4990.000001 + 8.000012995 = 134998.5J
So now for the final equation ~ Work Done divided by time ~ 134998.5 / 15 = 8999.900001 Watts
Which albeit is an extremely large amount of power, is just ever slightly under so the final answer is: No, Vegeta's power levels are not over 9000.