To determine the velocity and distance traveled by a particle of mass m under the influence of a constant force F, we need to consider Newton's second law of motion and apply the equations of motion.
Newton's second law states that the force acting on an object is equal to the mass of the object multiplied by its acceleration:
F = m * a
In this case, the force F is constant. Since the force is equal to mass times acceleration, we can rearrange the equation to solve for acceleration:
a = F / m
Now, let's consider the equations of motion for an object undergoing constant acceleration. These equations relate the initial velocity (u), final velocity (v), acceleration (a), time (t), and displacement (s) of the object. In this scenario, the force F is responsible for the acceleration.
Final velocity (v): v = u + a * t
Displacement (s): s = u * t + 0.5 * a * t^2
Now we can substitute the value of acceleration (a = F / m) into these equations:
Final velocity (v): v = u + (F / m) * t
Displacement (s): s = u * t + 0.5 * (F / m) * t^2
These equations allow us to calculate the velocity (v) and the distance traveled (s) after time (t), given the initial speed (u) and the constant force magnitude (F).