An elevator has a mass of 3000 kg If the upward tension in the supporting cable is 42000 N, how far does it rise in 2 seconds. assuming it begins at rest? a 13.5 m b 18m c 8.4 m d 5.5 m

## Step 1<br />The problem involves the principles of Newton's laws of motion and the concept of acceleration. The elevator is initially at rest, so its initial velocity is zero. The tension in the cable is greater than the weight of the elevator, which means the elevator is accelerating upwards. The acceleration can be calculated using Newton's second law, which states that the force equals mass times acceleration (F=ma).<br /><br />## Step 2<br />The weight of the elevator is its mass times the acceleration due to gravity (g), which is approximately 9.8 m/s². So, the weight of the elevator is 3000 kg * 9.8 m/s² = 29400 N.<br /><br />## Step 3<br />The net force acting on the elevator is the difference between the tension and the weight, which is 42000 N - 29400 N = 12600 N.<br /><br />## Step 4<br />Using Newton's second law, we can find the acceleration of the elevator. The acceleration is the net force divided by the mass, which is 12600 N / 3000 kg = 4.2 m/s².<br /><br />## Step 5<br />The elevator starts from rest, so its initial velocity is zero. The distance the elevator travels can be calculated using the equation of motion: distance = initial velocity * time + 0.5 * acceleration * time². Since the initial velocity is zero, the equation simplifies to distance = 0.5 * acceleration * time².<br /><br />## Step 6<br />Substituting the values of acceleration and time into the equation, we get distance = 0.5 * 4.2 m/s² * (2 s)² = 8.4 m.