Question Detail
Question
The position of a particle moving along the y-axis is given by y(t) = (t³ - 4t² + 6t) m, where y is in meters and t is in seconds. What is the object's displacement and average velocity for the time interval from t = 3 s to t = 5 s?
Correct Answer
Option A is the correct answer.
Detailed Explanation
y(3) = 27 - 36 + 18 = 9 m. y(5) = 125 - 100 + 30 = 55 m. Displacement = 55 - 9 = 46 m. Average velocity = displacement/time = 46/2 = 23 m/s. Option A says 46.0 m, 5.75 m/s (which is 46/8, not 46/2). Option B says 46.0 m, 23.0 m/s, which is correct.
Hint
Displacement = y(5) - y(3); average velocity = displacement/time interval.