Find the time dependence.... (Mechanics)

[Martyna]

Homework Statement

I am not looking for a solution to the problem, as much as I need a clarification on what it's asking for. The problem:

"A particle of mass m slides down an inclined plane under the influence of gravity. The particle is starting its motion from rest. Find the time dependence of the velocity, v(t) is the motion is resisted by a force F = kmf(v), with constant k for
1. f(v) = v^2. Find the time required to move a distance d.
2. f(v) = e^beta*v, where beta is a constant."

My question is what it means by find the time dependence. I know to find the time required to move a distance d, you must go backwards getting a solution for v(t) then x(t) then solving for t, however I'm unsure about what exactly is a "time dependence" kind of answer...?

 

[TSny]

Welcome to PF!

"Finding the time dependence of the velocity, v(t)" means to find the function v(t) which expresses v as a function of t.

For example, if a particle starts with velocity $v_0$ and moves along a straight line with constant acceleration $a$, then the time dependence of the velocity is expressed as the function $v(t) = v_0 + at$.

 

[Martyna]

Welcome to PF!

"Finding the time dependence of the velocity, v(t)" means to find the function v(t) which expresses v as a function of t.

For example, if a particle starts with velocity $v_0$ and moves along a straight line with constant acceleration $a$, then the time dependence of the velocity is expressed as the function $v(t) = v_0 + at$.

Of course...Just find v(t). I must have been misreading the problem confusing myself. Thank you!