Final answer:
A steel ball's total distance covered after its speed drops to half for the first time until it stops will be 28 cm, considering constant deceleration due to friction.
Step-by-step explanation:
The question pertains to kinematics and energy dissipation due to friction. Since the ball's speed halves after traveling 14 cm, we can assume that the deceleration due to friction is constant. Using similar deceleration, the ball will travel another 14 cm before its speed halves again from the speed it had at 14 cm, ultimately coming to a stop after traveling an additional 14 cm. Hence, the total distance the ball will cover after dropping to half of its speed for the first time until it stops is 14 cm + 14 cm = 28 cm.