In the relation a = 2v, where 'a' represents acceleration and 'v' represents velocity, we can determine the velocity as a function of time by integrating the acceleration with respect to time.
Let's assume that at t = 0, the velocity is v0. Then, integrating the given relation with respect to time, we have:
∫ a dt = ∫ 2v dt
Integrating both sides gives:
∫ a dt = ∫ 2v dt at = 2∫ v dt
Integrating the right side with respect to 't' gives:
at = 2 ∫ v dt at = 2vt + C
Here, 'C' represents the constant of integration, which arises due to the indefinite integration.
Now, solving for velocity 'v,' we get:
at = 2vt + C 2vt = at - C v = (at - C) / (2t)
The expression for velocity 'v' as a function of time 't' in the given relation a = 2v is:
v = (at - C) / (2t)
Please note that without specific initial conditions or information about the constant 'C,' it is not possible to determine the exact velocity as a function of time in this case.