Final answer:
To find the distance traveled while uniformly slowing down from 18.0 m/s to 6.0 m/s in 2.50 s, calculate the acceleration and then use the distance formula, resulting in 30 meters traveled.
Step-by-step explanation:
To calculate the distance traveled when you slow down uniformly from 18.0 m/s to 6.0 m/s over 2.50 seconds, you can use the formula for distance under uniform acceleration: d = v_i \( t) + \(1/2) a t^2, where v_i is the initial velocity, a is the acceleration, and t is the time. First, calculate the acceleration using the formula a = (v_f - v_i) / t. With an initial velocity (v_i) of 18.0 m/s, a final velocity (v_f) of 6.0 m/s, and time (t) of 2.50 s, the acceleration is a = (6.0 m/s - 18.0 m/s) / 2.50 s = -4.8 m/s^2 (negative because the object is slowing down).
Now, plug the values into the distance formula: d = (18.0 m/s)(2.50 s) + (1/2)(-4.8 m/s^2)(2.50 s)^2 = 45.0 m - 15.0 m = 30 m. Therefore, the distance traveled during this time is 30 meters, which corresponds to option A).