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?

1 Answer
Jan 25, 2016

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#