Final answer:
The object traveled 81.6 meters during the period of acceleration.
Step-by-step explanation:
To calculate the distance traveled by an object during a period of acceleration, you can use the equation:
displacement = initial velocity * time + (1/2) * acceleration * time^2
In this case, the object is starting with an initial velocity of 54.0 m/s and accelerating at -6.80 m/s². Since the object comes to a complete stop, the final velocity is 0 m/s. We can plug these values into the equation:
displacement = 54.0 m/s * t + (1/2) * (-6.80 m/s²) * t^2 = 0
By solving this quadratic equation, we find that the time it takes for the object to stop is approximately 7.94 seconds. To calculate the distance, we can substitute this value back into the equation:
displacement = 54.0 m/s * 7.94 s + (1/2) * (-6.8 m/s²) * (7.94 s)^2 = -81.6 meters
Since distance cannot be negative, the object traveled a distance of 81.6 meters during that period.