The relation between kinetic and potential energy

The potential energy is the energy accumulated in an object by its location.

PE = mgh where, m - mass, g - acceleration due to gravity and h - height

The energy possessed by an object as a result of its motion is known as kinetic energy.

KE = \frac{1}{2} mv^2   Where, m-mass and v- velocity  

Energy cannot be destroyed, only converted from one form to another, according to the law of conservation of energy.

PE begins from 0 at the projection point and increases to a maximum value at a constant speed at maximum height.

KE begins at the projection point with a maximum value and decrease constantly to 0 at maximum height.

Total energy = PE + KE.

At the maximum height (when object dropped): PE = KE  

Step 1: Set up an equation for the speed of the train

Given that

Mass of the train m = 2.5 kg

Energy stored in the spring due to compression by the train, PE = 0.48 joules

When train starts

The amount of potential energy stored by spring is equal to the kinetic energy of the train.

PE = KE

PE = \frac{1}{2}mv^2

v = \sqrt{\frac{2 * PE}{m}}

Step 2:  Determine the initial velocity of the train

v = \frac{2* 0.48}{2.5}

v = 0.384

Hence, initial speed of the train v = 0.384 m/s