Get time from acceleration given as a function of velocity

1. Oct 20, 2015

harmyder

1. The problem statement, all variables and given/known data
If the acceleration is given as a function of velocity a(v), we can found t(v) as t(v) = t0 + ∫vv0 1/a(v) dv.

2. Relevant equations

3. The attempt at a solution
I just can't understand there to go to understand the equation..

2. Oct 20, 2015

Staff: Mentor

What is the (calculus based) definition of acceleration?

3. Oct 21, 2015

harmyder

$$\frac{dv}{dt} = a(t) \rightarrow v(t_1) = v(t_0) + \int_{t_0}^{t_1}a(t)dt$$
$$\frac{dt}{dv} = \frac{1}{a(t)} \rightarrow t(v_1) = t(v_0) + \int_{v_0}^{v_1}\frac{1}{a(t)}dv$$

but it is still not $a(v)$

4. Oct 21, 2015

Nathanael

How will you integrate f(t)dv? t and v are not independent variables.

Note that acceleration a is dv/dt regardless of if a is a function of time a(t) or a function of velocity a(v)