If a 0.50-kg block initially at rest on a frictionless, horizontal surface is acted upon by a force of 7.6 N for a distance of 8.6 m, then what would be the block's velocity

the work ... 7.6N * 8.6m

... is equal to the block's KE

1/2 * 0.50 * v^2 = 7.6 * 8.6

To find the velocity of the block, we can use Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration.

The formula for calculating acceleration is:
acceleration = force / mass

Given that the force acting on the block is 7.6 N and its mass is 0.50 kg, we can calculate the acceleration:
acceleration = 7.6 N / 0.50 kg

Now, we need to calculate the distance covered by the block. Since the block is initially at rest and a constant force is applied to it, we can use the work-energy principle to find the distance covered:
work = force × distance

Given that the force acting on the block is 7.6 N and the distance covered is 8.6 m, we can calculate the work done on the block:
work = 7.6 N × 8.6 m

The work done on the block is equal to its change in kinetic energy, so we can use this relationship to find the final velocity of the block.

Kinetic energy = (1/2) × mass × velocity^2

By equating the work done to the change in kinetic energy, we can solve for the final velocity of the block.

(1/2) × mass × velocity^2 = work

Now, let's calculate step by step:

1. Calculate the acceleration:
acceleration = 7.6 N / 0.50 kg

2. Calculate the work done on the block:
work = 7.6 N × 8.6 m

3. Calculate the change in kinetic energy:
(1/2) × mass × velocity^2 = work

4. Solve for velocity by rearranging the equation:
velocity = √(2 × work / mass)

Substituting the known values into the equation will give you the final velocity of the block.