The Acceleration of a Moving Object Is Given By $\frac{d^{2} x}{d t^{2}}=x\left(\frac{d x}{d t}-1\right)$

Multiple Choice

The acceleration of a moving object is given by $\frac{d^{2} x}{d t^{2}}=x\left(\frac{d x}{d t}-1\right)$ where x(t) is the position at time t.Which of the following is a system of first order differential equations for position x and velocity v?

A) $v=\frac{d x}{d t}, \frac{d v}{d t}=x(1-v)$
B) $v=\frac{d x}{d t}, \frac{d v}{d t}=v-1$
C) $v=\frac{d x}{d t}, \frac{d v}{d t}=x(v-1)$
D) $v=\frac{d x}{d t}, \frac{d v}{d t}=\frac{x^{2}}{2}(v-1)$