This computer science problem involves algorithmic thinking and programming concepts. The solution below explains the approach, logic, and implementation step by step.
ScanSolve AI Answer
Step 1: Identify the position vector function. The position of the particle as a function of time is given by: r(t) = [(5.0)t + (6.0)t^2]i + [(7.0) - (3.0)t^3]j Step 2: Calculate the position vector at t_1 = 2.0 s. Substitute t = 2.0 s into the position function: r(2.0) = [(5.0)(2.0) + (6.0)(2.0)^2]i + [(7.0) - (3.0)(2.0)^3]j r(2.0) = [10.0 + (6.0)(4.0)]i + [7.0 - (3.0)(8.0)]j r(2.0) = [10.0 + 24.0]i + [7.0 - 24.0]j r(2.0) = (34.0i - 17.0j)\, m Step 3: Calculate the position vector at t_2 = 3.0 s. Substitute t = 3.0 s into the position function: r(3.0) = [(5.0)(3.0) + (6.0)(3.0)^2]i + [(7.0) - (3.0)(3.0)^3]j r(3.0) = [15.0 + (6.0)(9.0)]i + [7.0 - (3.0)(27.0)]j r(3.0) = [15.0 + 54.0]i + [7.0 - 81.0]j r(3.0) = (69.0i - 74.0j)\, m Step 4: Calculate the displacement vector. Displacement r is the change in position, given by r = r(t_2) - r(t_1). r = r(3.0) - r(2.0) r = (69.0i - 74.0j) - (34.0i - 17.0j) r = (69.0 - 34.0)i + (-74.0 - (-17.0))j r = (35.0)i + (-74.0 + 17.0)j r = (35.0i - 57.0j)\, m Step 5: Compare the result with the given options. The calculated displacement is (35i - 57j) m, which matches option (A). The final answer is A) (35i - 57j)\, m. That's 2 down. 3 left today — send the next one.