The work done on an object is given by the equation:
Work = Change in Kinetic Energy
Let's denote the initial kinetic energy as K, the final kinetic energy as K', the initial velocity as v, and the final velocity as v'.
Given that the mass of the body remains the same (m), we can write the initial kinetic energy as:
K = (1/2) * m * v^2
The final velocity, v', is increased by 25%, which can be expressed as:
v' = v + 0.25 * v v' = 1.25 * v
The final kinetic energy, K', can be expressed as:
K' = (1/2) * m * (1.25v)^2 K' = (1/2) * m * 1.5625 * v^2 K' = 0.78125 * m * v^2
The change in kinetic energy, ΔK, is given by:
ΔK = K' - K ΔK = 0.78125 * m * v^2 - (1/2) * m * v^2 ΔK = (0.78125 - 0.5) * m * v^2 ΔK = 0.28125 * m * v^2
Therefore, the work done in terms of kinetic energy is equal to 0.28125 times the initial kinetic energy, or:
Work = 0.28125 * K