A box is sliding along a frictionless surface and gets to a ramp. Disregarding friction, how fast should the box be going on the ground in order to slide up the ramp to a height of 2.5 meters, where it stops? (Use g = 9.8 m/s2.)

You have velocity final, distance, acceleration, but you need the velocity initial

vf^2 = vi^2 + 2ad

flip the vf^2 and vi^2 because you're searching for vi

vi = (vf is zero because it comes to a stop) + square root of 2ad

vi = the square root of 2ad

= square root of 2 (9.8m/s^2) (2.5m)

vi = 7 m/s