The change in its kinetic energy.
Explanation
The relationship between the work done on an object and the change in its speed is governed by the Work-Energy Theorem. This principle states that the net work done on a rigid body by all forces acting on it is equal to the change in the kinetic energy of the body.
Option Analysis
- The change in its potential energy. is incorrect: The change in potential energy is related to the work done against conservative forces (like gravity or spring force) and depends on the position or configuration of the object, not primarily on its velocity.
- The change in its kinetic energy. is correct: Kinetic energy ($K$) is defined as $\frac{1}{2}mv^2$. According to the Work-Energy Theorem, the work done ($W$) results in a change in kinetic energy:
$W = K_{final} - K_{initial} = \frac{1}{2}mv^2 - \frac{1}{2}mu^2$
Therefore, the work done to change velocity from $u$ to $v$ corresponds to the change in kinetic energy. - The product of force and time. is incorrect: The product of force and time ($F \times t$) is defined as Impulse. According to Newton's Second Law, impulse is equal to the change in momentum ($\Delta p$), not work. Work is defined as the product of force and displacement.
- The sum of its initial and final momentum. is incorrect: The sum of initial and final momentum is not a standard physical quantity associated with work done.
Key Takeaway
Work-Energy Theorem: The work done by the net force on a particle is equal to the change in its kinetic energy ($W = \Delta K$).