Understanding the Concepts

* Initial Velocity (v₀): The runner's starting speed, which is 4 meters per second.

* Final Velocity (v): We don't know the final velocity directly, but we can figure it out.

* Time (t): The time elapsed is 20 seconds.

* Displacement (Δx): The change in position is 6 meters.

* Acceleration (a): The rate at which the runner's velocity changes.

Calculations

1. Find the Final Velocity (v):

We can use the equation: Δx = v₀t + (1/2)at²

Since we don't know the acceleration (a) yet, we can rearrange this equation to solve for the final velocity (v):

v = (Δx - (1/2)at²) / t

v = (6 - (1/2) * a * 20²) / 20

v = (6 - 200a) / 20

2. Calculate Acceleration (a):

Now we can use the definition of acceleration: a = (v - v₀) / t

Substitute the expression for v we found:

a = (((6 - 200a) / 20) - 4) / 20

Simplify and solve for a:

a = (6 - 200a - 80) / 400

400a = -74 - 200a

600a = -74

a ≈ -0.123 meters per second squared

Conclusion

The runner's acceleration is approximately -0.123 meters per second squared. The negative sign indicates that the runner is decelerating (slowing down).