Final answer:
Using the kinematic equations with the given acceleration and final velocity, the boxcar will travel approximately 22.86 meters.
Step-by-step explanation:
To find out how far a boxcar will travel starting from rest and reaching an acceleration of 13.1 m/s² and a velocity of 24.5 m/s, we need to use the kinematic equations that relate distance, acceleration, and velocity. The formula s = vt - 0.5at², where s is the distance, v is the final velocity, t is the time, and a is the acceleration, can be used to solve for s.
First, we need to calculate the time using v = at, which gives us t = v/a. Substituting the values into this equation, we find t = 24.5 m/s / 13.1 m/s² ≈ 1.87 s. Next, we calculate the distance s using the first equation: s = (24.5 m/s)(1.87 s) - 0.5(13.1 m/s²)(1.87 s)² ≈ 22.86 m.
Therefore, the boxcar will travel approximately 22.86 meters.