I do not understand how to find the GPE and KE without velocity.

At point A;

GPE = 58800 J

KE = 0 J

At point B;

GPE = 44100 J

KE = 14700 J

At point C;

GPE = 0 J

KE = 58800 J

At point D;

GPE = 29400 J

KE = 29400 J

EPE = 29400 J.

Explanation:

The Gravitational Potential Energy, GPE, is given as follows;

GPE = The mass. m × The acceleration due to gravity, g × The elevation or height, h

∴ GPE = m × g × h

The Kinetic Energy, KE = 1/2  × The mass × The square of the velocity, v²

KE = 1/2 × m × v²

At point A;

The parameters are;

h = 100m, v = 0 (Starting point), Cart mass, m = 60 kg, we have;

GPE = m × g × h = 60 × 9.8 × 100 = 58800

GPE = 58800 J

KE = 1/2 × m × v² = 1/2 × 60 × 0² = 0

KE = 0 J

Mechanical Energy, ME = GPE + KE = 58800 + 0 = 58800 = Constant

ME = 58800 J

At point B;

GPE = 60 × 9.8 × 75 = 44100

GPE = 44100 J

KE = ME - GPE = 58800 - 44100 = 14700

KE = 14700 J

At point C;

GPE = 60 × 9.8 × 0 = 0 J

KE = ME - GPE = 58800 - 0 = 58800

KE = 58800 J

At point D;

v = 0, the Cart is brought to rest by the spring

GPE = 60 × 9.8 × 50 = 29400

GPE = 29400 J

KE = ME - GPE = 58800 - 29400 = 29400

KE = 29400 J

The Elastic Potential Energy EPE gained by the spring = KE = 29400

EPE = 29400 J.

your answer would be fusion