This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here's the solution for the object's displacement and average velocity: The position of the particle is given by y(t) = (t^3 - 4t^2 - 6t)m. We need to find the displacement and average velocity for the time interval from t = 3s to t = 5s. Step 1: Calculate the position at t = 3s. Substitute t=3 into the position function: y(3) = (3^3 - 4(3^2) - 6(3))m y(3) = (27 - 4(9) - 18)m y(3) = (27 - 36 - 18)m y(3) = (-9 - 18)m y(3) = -27m Step 2: Calculate the position at t = 5s. Substitute t=5 into the position function: y(5) = (5^3 - 4(5^2) - 6(5))m y(5) = (125 - 4(25) - 30)m y(5) = (125 - 100 - 30)m y(5) = (25 - 30)m y(5) = -5m Step 3: Calculate the displacement ( y). Displacement is the change in position, y = y(t_2) - y(t_1). y = y(5) - y(3) y = (-5m) - (-27m) y = -5m + 27m y = 22m The object's displacement is 22 m. Step 4: Calculate the average velocity (v_avg). Average velocity is the displacement divided by the time interval, v_avg = ( y)/( t). The time interval is t = 5s - 3s = 2s. v_avg = 22m2s v_avg = 11m/s The object's average velocity is 11 m/s.