Chapter 2, Problem 42P

The kinematic equations can describe phenomena other than motion through space and time. Suppose x represents a person’s bank account balance. The units of x would be dollars ($), and velocity v would give the rate at which the balance changes (in units of, for example, $/month). Acceleration would give the rate at which v changes. Suppose a person begins with ten thousand dollars in the bank. Initial money management, leads to no net change in the account balance so that v₀ = 0. Unfortunately, management worsens over time so that a = −2.5 × 10² $/month². Assuming a is constant, find the amount of time in months until the bank account is empty