Calculus Based Questions: Practice Problem & Solution

Solution Explained:

To solve this problem, we apply the core principles of Calculus Based Questions. Understanding the underlying formula is key to arriving at the correct answer below:

Given \(x = (t + 5)^{-1}\). Velocity \(v = \frac{dx}{dt} = -(t + 5)^{-2}\). Acceleration \(a = \frac{dv}{dt} = 2(t + 5)^{-3}\). From \(v = -(t + 5)^{-2}\), we have \((t+5)^{-1} = ((-v)^{-1/2})\). So \(a = 2((t+5)^{-1})^3 = 2((-v)^{-1/2})^3 = 2(-v)^{3/2}\). Thus, \(a \propto (\text{Velocity})^{3/2}\).