Question

The power needed to accelerate a projectile from rest to its launch speed v in a time t is 47.8 w. How much power is needed to accelerate the same projectile from rest to a launch speed of 2v in a time of t?

Answer 1

#BAL

not dealing with potential energy, only wit kinetic energy:

Power = energy / time  

the kinetic energy, or work done, when the final velocity is reached is in the first case

Ekin 1 = 1/2 mv^2  

and the Power needed is Ekin/t = 1/2 mv^2/t

the power in the second case is

P = 1/2 m(2v)^2/(t/2) = 4*2*(1/2 mv^2/t)  

so a 8 fold power is necessary: Power = 8*32W = 256 W