1. Understand the Concepts

* Uniform acceleration: The ball's speed increases at a constant rate.

* Equations of motion: We'll use the following equation to relate displacement (distance), initial velocity, acceleration, and time:

* d = v₀t + (1/2)at²

* where:

* d = displacement (250 m)

* v₀ = initial velocity (0 m/s, since the ball starts at rest)

* t = time (5 s)

* a = acceleration (what we want to find)

2. Solve for Acceleration

* Plug the known values into the equation:

* 250 = (0)(5) + (1/2)a(5)²

* Simplify:

* 250 = (1/2)a(25)

* 250 = 12.5a

* Solve for 'a':

* a = 250 / 12.5

* a = 20 m/s²

3. Calculate Final Velocity

* We can use another equation of motion to find the final velocity:

* v = v₀ + at

* Plug in the values:

* v = 0 + (20)(5)

* v = 100 m/s

Therefore:

* Acceleration of the ball: 20 m/s²

* Final velocity of the ball: 100 m/s