# Power from Acceleration

1. Apr 11, 2006

### BH_1984

I am trying to work out power from acceleration and mass alone. But i'm having a mind blank with regard to the actual calculation and it is driving me crazy.

Force = Mass x Acceleration
Work = Mass x Acceleration x Distance
Power = Work / Time
Power = Mass x Acceleration x Velocity
Hence: Power = Mass x Acceleration x Integration of Acceleration

So from this what should the Power be for the following situation?

Mass = 5 Kg
Acceleration at t = 0 sec is 4.2 ms^-2
Acceleration at t = 0.2 sec is 8.4 ms^-2

Does a point need to be interpolated on the line to work the acceleration
and integration of acceleration before it can be placed into the equation?
Plus as the time between the two values is 0.2 sec does the answer need to be multiplied by 5?

Thanks
BH

2. Apr 12, 2006

### Andrew Mason

Since power is the time rate of change of energy, find the change in energy of the mass. Assume the KE of the mass at t=0 is 0.

I think you have to assume that the rate of change of acceleration, a', is constant over the ensuing .2 seconds. So use: a = a't where a' = constant ($a' = \Delta a/\Delta t$). This makes v a second order term:

$$v = \int_{t=0}^{t=.2} a'tdt = \frac{1}{2}a't^2$$

AM

Last edited: Apr 12, 2006
3. Apr 12, 2006

### BH_1984

Thanks Andrew, I think I have solved it now