To determine the velocity and distance traveled by a particle of mass m under the influence of a constant force F, we can use the equations of motion. Let's assume that the force is applied in the positive direction along the straight line.
- Velocity (v): The equation of motion relating velocity (v), initial velocity (u), time (t), and acceleration (a) is given by:
v = u + at
Since the force F is constant, we can use Newton's second law, which states that force (F) is equal to mass (m) multiplied by acceleration (a). Therefore:
F = ma
Rearranging the equation, we get:
a = F/m
Substituting this value of acceleration (a) in the equation of motion, we have:
v = u + (F/m)t
- Distance traveled (s): The equation of motion relating distance traveled (s), initial velocity (u), time (t), and acceleration (a) is given by:
s = ut + (1/2)at²
Substituting the value of acceleration (a) from Newton's second law, we have:
s = ut + (1/2)(F/m)t²
Now you have the equations for velocity and distance traveled. You can use these equations to calculate the values after time t, given the mass (m), initial speed (u), and force magnitude (F).