Question

What is the velocity in terms of time if it moves by the relation a=2v?

Answer 1

If the relation between acceleration (a) and velocity (v) is given by $a=2v$, we can determine the velocity as a function of time. To do this, we need to integrate the acceleration with respect to time.

Let's assume that at $t=0$, the velocity is $v_0$.

The relation $a=2v$ implies that $\frac{dv}{dt}=2v$. Rearranging the equation, we have $\frac{dv}{v}=2dt$.

Integrating both sides:

$\int \frac{dv}{v}=\int 2dt$

Using the properties of integration, we get:

$\ln |v|=2t+C$

where $C$ is the constant of integration.

Taking the expon