Final answer:
The patient's bed will be moving at a speed of 2.625 m/s after 7 seconds under a constant force of 30 N.
Step-by-step explanation:
A nurse pushes a patient’s bed with a constant force of 30 N. The bed with a mass of 80 kg was originally at rest. To determine how fast the bed is moving after 7 seconds, we need to use Newton's Second Law of Motion which states that acceleration is the force applied divided by the mass of the object (a = F/m). The calculated acceleration is a = 30 N / 80 kg = 0.375 m/s². Since the bed was initially at rest, we can also use the formula for uniform acceleration, v = u + at, where v is the final velocity, u is the initial velocity (which is 0 m/s since the bed was at rest), a is the acceleration, and t is the time. Plugging in the values we have, v = 0 m/s + (0.375 m/s²)(7 s) = 2.625 m/s.