If a roller coaster train has a potential energy of 1,500 j and a kinetic energy of 500 j as it starts to travel downhill, its total energy is

there are no components of a physical goal mentioned on the list of choices that you've provided.

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft