A body is moved along a straight line by a machine delivering constant power. The distance moved by the body in time t is proportional to

When a machine applies constant power to move a body along a straight line, one may understand the relation of the distance covered by the body with time through the concept of power. Power is the rate of doing work or transferring energy. When the machine gives constant power, it means that the energy being given to the body remains constant with respect to time.

When the body moves, its velocity increases due to the continuous supply of energy. When the velocity of the body increases, the force acting upon it decreases because the product of force and velocity must remain constant in order to keep the power constant. This variation in force and velocity affects the distance traveled by the body over time.

Analysis of the dynamics of the motion, taking place under constant power, reveals that the distance moved by the body is proportional to t³/². The relation can be derived from the basic principles of work, energy, and motion in a system of force, velocity, and time.

Thus, the motion of the body shows how the distance traveled varies as a function of time when constant power is being delivered; it highlights the relationship between energy transfer and motion characteristics.

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