Proportionality of Velocity Acquired by a Mass
The velocity acquired by a mass in traveling a certain distance under the action of a constant force is directly proportional to several factors.

Force Applied
- The force applied to the mass plays a crucial role in determining the velocity acquired. According to Newton's second law of motion, F = ma, where F is the force, m is the mass, and a is the acceleration. The acceleration produced by the force will determine how quickly the mass gains velocity.

Distance Traveled
- The distance traveled by the mass also affects the velocity acquired. As the distance increases, the mass has more time to accelerate under the constant force, resulting in a higher final velocity.

Time Taken
- The time taken to travel the distance is another factor that influences the velocity acquired. A longer time period allows the mass to gradually build up velocity, while a shorter time period may result in a lower final velocity.

Friction and Other Resistive Forces
- The presence of friction and other resistive forces can impact the velocity acquired by a mass. These forces oppose the motion of the mass, reducing the overall acceleration and final velocity.
In conclusion, the velocity acquired by a mass in traveling a certain distance under the action of a constant force is directly proportional to the force applied, distance traveled, time taken, and inversely proportional to friction and other resistive forces. By understanding these factors, one can predict and analyze the velocity acquired by a mass in various scenarios.