Final answer:
The work-energy theorem states that the work done on an object by a force over a distance is equal to the change in the object's kinetic energy. By applying a constant force along the direction of motion, all the work contributes to increasing the object's kinetic energy. Thus, the increase in kinetic energy is equal to the work done by the force.
Step-by-step explanation:
To prove that the increase in kinetic energy of a body moving in a straight line is equal to the work done by the force on the body, we can reference the work-energy theorem. This theorem states that the net work done on an object is equal to the change in that object's kinetic energy. Kinetic energy is given by the equation KE = 1/2mv², where m is the mass and v is the velocity.
Considering a force f applied over a distance d, work W is defined as W = fd. If this force causes the velocity of the body to change, the work done on the body will cause a change in kinetic energy. This change can be calculated as ΔKE = KEfinal - KEinitial, where KEfinal = 1/2mvfinal² and KEinitial = 1/2mvinitial².
Since the force is applied in the direction of motion, all of the work contributes to increasing the velocity and kinetic energy. Hence, the work done by the force is equal to the increase in kinetic energy of the body, confirming the consistency of the work-energy theorem. Whether the work done is positive or negative will depend on the direction of the force relative to the object's motion.