Ahammer is thrown upward with a speed of 14 m/s on the surface of planet x where the acceleration due to gravity is 3.5 m/s2 and there is no atmosphere. what is the speed of the hammer after 8.0 s?

Pretty simple

The no atmosphere says that theres no air resistance, making the problem 10 times easier.

If the hammer is thrown upwards, it has a positive inital velocity of 14m/s

Now gravity is trying to pull it downwards so the accelerating is -3.5m/s^2 (closest planet I can think off with this acceleration is Mercury, but thats besides the point)

Anyways we can use kinematic equations to solve that

Vf = vi + at

Vf = 14m/s +(-3.5)(8)

Vf = -14 m/s

So after 8 seconds the ball is going downwards at the same height that you threw it.

answer : -14m/s or you can say 14m/s downwards

change tension