A 49 kg lady stands on a spring scale in an elevator. During the first 5 sec, starting from rest, the scale reads 69 kg. The velocity of the elevator will be A. 10 m/sec B. 15 m/sec C. 20 m/sec D. 25 m/sec

The correct answer is $\boxed{\text{B) 15 m/sec}}$.

The scale reads 69 kg, which means that the force of the scale on the lady is 69 N. This force is equal to the lady’s weight plus the force of the elevator’s acceleration on her. The lady’s weight is 49 N, so the force of the elevator’s acceleration on her is 20 N. This means that the elevator is accelerating at 20 N / 49 kg = 0.41 m/s^2. After 5 seconds, the velocity of the elevator is 0.41 m/s^2 * 5 s = 2.05 m/s.

Here is a brief explanation of each option:

• Option A: 10 m/sec. This is the velocity of the elevator after 5 seconds if it were accelerating at a constant rate of 10 m/s^2. However, the scale reads 69 kg, which means that the elevator is accelerating at a rate of 0.41 m/s^2.
• Option B: 15 m/sec. This is the correct answer.
• Option C: 20 m/sec. This is the velocity of the elevator after 5 seconds if it were accelerating at a constant rate of 20 m/s^2. However, the scale reads 69 kg, which means that the elevator is accelerating at a rate of 0.41 m/s^2.
• Option D: 25 m/sec. This is the velocity of the elevator after 5 seconds if it were accelerating at a constant rate of 25 m/s^2. However, the scale reads 69 kg, which means that the elevator is accelerating at a rate of 0.41 m/s^2.