**Finding the Upward Acceleration:**

To find the upward acceleration of the elevator, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the force acting on the elevator is the tension in the supporting cable.

The equation to calculate the acceleration is:

Force = mass × acceleration

Rearranging the equation to solve for acceleration:

Acceleration = Force / mass

Substituting the given values:

Acceleration = 50,000N / 5000kg

Acceleration = 10 m/s²

Therefore, the upward acceleration of the elevator is 10 m/s².

**Calculating the Distance Traveled:**

To find the distance traveled by the elevator in a time of 10 seconds, we can use the equation of motion for uniformly accelerated linear motion:

Distance = Initial velocity × time + (1/2) × acceleration × time²

Since the elevator starts from rest, the initial velocity is 0.

Substituting the given values:

Distance = 0 × 10 + (1/2) × 10 m/s² × (10 s)²

Distance = 0 + (1/2) × 10 m/s² × 100 s²

Distance = 0 + 5 m/s² × 100 s²

Distance = 500 m

Therefore, the elevator rises a distance of 500 meters in a time of 10 seconds, starting from rest.

**Explanation:**

The tension in the supporting cable is equal to the force acting on the elevator. By using Newton's second law of motion, we can calculate the upward acceleration of the elevator. In this case, the upward acceleration is found to be 10 m/s².

To find the distance traveled by the elevator in a given time, we can use the equation of motion for uniformly accelerated linear motion. Since the elevator starts from rest, the initial velocity is 0. By substituting the given values into the equation, we find that the elevator rises a distance of 500 meters in a time of 10 seconds.

It is important to note that the calculations assume ideal conditions and do not take into account factors such as friction or air resistance.