Question

The acceleration of a sphere falling through a liquid is \( (30 - 3y) \, \text{cm/s}^2 \) where \( y \) is speed in cm/s. The maximum possible velocity of the sphere and the time when it is achieved are

• A. 10 cm/s after 10 second
• B. 10 cm/s instantly
• C. 10 cm/s, will never be achieved
• D. 30 cm/s, after 30 second

Hint:

To find the maximum velocity in problems involving acceleration with respect to speed, solve the differential equation for velocity.

Answer 1

The Correct Option is D

Step 1: Analyze the equation.
The velocity of the sphere can be found by solving the differential equation given by \( a = \frac{dv}{dt} = 30 - 3v \).
Step 2: Conclusion.
Thus, the maximum velocity is 30 cm/s, achieved after 30 seconds.
Final Answer: \[ \boxed{30 \, \text{cm/s, after 30 second}} \]