Question

If a rocket with a mass of `3500` tons vertically accelerates at a rate of `1/2 m/s^2`, how much power will the rocket have to exert to maintain its acceleration at 12 seconds?

Answer 1

General formula: `E = 1/2Ma^2t^2`
With data provided: `E = 1/2*3500000*(1/2)^2*12^2 = 63,000,000J`

Explanation:

The amount of energy `E` the rocket has to exert, considering its mass `M` is constant (ignoring the loss of mass of burnt fuel) and it's moving with the same acceleration `a`, equals to a product of a force `F` its engine pushes the rocket upward and a distance `l` it goes:
`E = F*l`

The force `F` can be calculated using the Second Law of Newton:
`F = M*a`

The distance `l` can be calculated using the formula for the distance as a function of time with zero initial speed and a constant acceleration:
`l = 1/2at^2`

From that we conclude:
`E = 1/2Ma^2t^2`

With data provided in the problem:
`E = 1/2*3500000*(1/2)^2*12^2 = 63,000,000J`