Final answer:
To find the distance an elevator has risen in 3 seconds from rest, one must calculate the net force from the tension in the cable minus the weight, determine the acceleration, and then apply the second equation of motion.
Step-by-step explanation:
The question involves calculating the distance traveled by an elevator in 3 seconds when it starts from rest with a given tension in the cable. To solve this, we use the second equation of motion (s = ut + 1/2at²) where 'u' is the initial velocity, 'a' is the acceleration, and 't' is time. Since the elevator starts from rest, the initial velocity u = 0. The tension in the cable provides the force for the elevator to move upwards, which is used to calculate the acceleration.
First, we find the net force acting on the elevator using Newton's second law (Net force = tension - weight), where the weight is the product of mass and gravitational acceleration (W = mg). Then the acceleration 'a' is found by dividing this net force by the mass of the elevator (a = Net force / m). Lastly, we can substitute the calculated 'a' and the given 't' into the motion equation to find the distance 's'.