Two identical disks A and B can spin around vertical axes. Disk A is spinning with an initial angular speed of 40 rev/s when its rim touches initially stationary disk B, causing that disk to begin to spin. The rubbing at the contact point slows A while speeding up B. The rate at which both disks change their angular speeds is `2.0rev//s^(2)`. Find the time required for the two disks to reach the same angular speed.

Explanation

To solve the problem, we need to find the time required for the two disks A and B to reach the same angular speed after they start rubbing against each other.

**Step 1: Define the initial conditions.**
- Disk A has an initial angular speed \( \omega_A = 40 \, \text{rev/s} \).
- Disk B is initially stationary, so \( \omega_B = 0 \, \text{rev/s} \).
- The rate at which both disks change their angular speeds is given as \( 2.0 \, \text{rev/s}^2 \).

**Step 2: Write the equations for the angular speeds of both disks over time.**
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