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

question 117

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) \(v=\frac{d x}{d t}, \frac{d v}{d t}=\frac{x^{2}}{2}(v-1)\)

---

Definitions:

Lien Theory

A concept in real estate law where the mortgage holder has a lien on the property as security for the underlying loan, but the borrower retains title to the property.

Title Theory

Title theory pertains to mortgage law where the mortgage lender holds title to the mortgaged property until the borrower has fully paid off the loan.

Mortgages

Legal agreements in which a lender lends money at interest in exchange for taking title of the borrower's property, with the condition that the conveyance of title becomes void upon the payment of the debt.

Mortgage

A legal agreement by which a bank, credit union, or other lender lends money at interest in exchange for taking title of the borrower's property, with the condition that the conveyance of title becomes void upon the payment of the debt.