This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Step 1: Identify the formula for work done by a variable force. The work done W by a variable force F_x acting along the x-axis from position x_1 to x_2 is given by the integral: W = _x_1^x_2 F_x\,dx Given F_x = (14x - 3.0x^2) N, x_1 = -1 m, and x_2 = +2 m. Step 2: Set up the definite integral. Substitute the given force function and limits of integration into the formula: W = _-1^2 (14x - 3x^2)\,dx Step 3: Evaluate the integral. Integrate each term with respect to x: W = [ 14x^1+11+1 - 3x^2+12+1 ]_-1^2 W = [ (14x^2)/(2) - (3x^3)/(3) ]_-1^2 W = [ 7x^2 - x^3 ]_-1^2 Step 4: Apply the limits of integration. Substitute the upper limit (x=2) and subtract the result of substituting the lower limit (x=-1): W = (7(2)^2 - (2)^3) - (7(-1)^2 - (-1)^3) W = (7(4) - 8) - (7(1) - (-1)) W = (28 - 8) - (7 + 1) W = 20 - 8 W = 12 \, J The work done is +12 J. Comparing this with the given options, it matches option e. The final answer is e. +12 J. Send me the next one 📸