physics
posted by Zach .
When a 1150 kg space rocket lifts off of ground. How many joules of energy has been provided by its engine during the time in which it achieves a speed of 180 m/s.

I don't see a solution here. Much of the energy of the lift is just providing a force mg which holds the rocket off the ground, not incuding an upward acceleration. So the time to accelerate, or the acceleration itself it critical.
You can ignore this, and compute
final KE: 1/2 mv^2
final PE= mgh=mg (v/2)*time
but you are still left with not knowing the time it took to get to v. Of course, the energy of the rocket provides final PE+final KE.