# Motion under influence of a resistive force

No template because originally posted in wrong thread
Consider the 1d motion of a body under the influence of the force given by F = -m*γ*vα. m is mass, γ is a constant of appropriate dimension, v is velocity and α is dimensionless constant. The value of α for which the motion will come to a stop in finite time is to be calculated. I solved the equation of motion given by v'' = -γ*vα and got an equation for t given by t = (1/γ)*(V01-α)/(1-α); V0 is the initial velocity. According to this, for all γ>1, time is finite. But the sign of t is negative. Why is this happening? Am I doing something wrong?

## Answers and Replies

Chestermiller
Mentor
Your solution for t is correct. What do you get for t if ##\alpha = 0##? Is this a finite time? Is it positive?

Your solution for t is correct. What do you get for t if ##\alpha = 0##? Is this a finite time? Is it positive?
For ##\alpha = 0## it is positive but what about something like α = 2? It is turning out to be negative unless I am mistaken. right?

Chestermiller
Mentor
For ##\alpha = 0## it is positive but what about something like α = 2? It is turning out to be negative unless I am mistaken. right?
Yes. That's the region that is not physically realistic.

What do you get when ##\alpha = -1##? Is that a finite time? What do you get for v vs t in the special case when ##\alpha = 1##?