Final answer:
The scale reading during the elevator's acceleration can be found by adding the man's weight and the additional force due to the elevator's acceleration. The weight of the man is 735 N, and the additional force due to acceleration is 1125 N, for a total of 1860 N, which is higher than any of the provided options, suggesting a mistake in the options listed.
Step-by-step explanation:
Calculating Scale Reading During Acceleration
To determine the scale reading when the man is in an accelerating elevator, we will calculate the apparent weight. First, let's find the acceleration of the elevator. The elevator accelerates uniformly from rest to 30.0 m/s in 2.00 s, so:
a = Δv / Δt = (30.0 m/s) / (2.00 s) = 15.0 m/s²
The apparent weight is the sum of the real weight and the force due to the acceleration of the elevator (mass times the acceleration, F = ma).
Weight = mg = (75.0 kg)(9.8 m/s²) = 735 N
Additional force due to acceleration = ma = (75.0 kg)(15.0 m/s²) = 1125 N
Therefore, the scale reading is the sum of the weight and the additional force:
Scale reading = Weight + Additional force = 735 N + 1125 N = 1860 N
This is more than the options provided, indicating a potential error in the options listed.