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
You're on a roll — To determine the stopping distance of the car, we will use the work-energy theorem, which states that the net work done on an object is equal to the change in its kinetic energy. Given values: • Mass of the car, m = 1300 kg • Initial speed of the car, v_i = 13.3 m · s^-1 • Final speed of the car (when it stops), v_f = 0 m · s^-1 • Frictional force, F_f = 7700 N Step 1: State the work-energy theorem. W_net = KE W_net = KE_f - KE_i Step 2: Calculate the initial and final kinetic energies. The formula for kinetic energy is KE = (1)/(2)mv^2. Initial kinetic energy: KE_i = (1)/(2)mv_i^2 KE_i = (1)/(2)(1300 kg)(13.3 m · s^-1)^2 KE_i = (1)/(2)(1300 kg)(176.89 m^2 · s^-2) KE_i = 650 kg · 176.89 m^2 · s^-2 KE_i = 114978.5 J Final kinetic energy: KE_f = (1)/(2)mv_f^2 Since the car stops, v_f = 0 m · s^-1. KE_f = (1)/(2)m(0)^2 = 0 J Step 3: Calculate the work done by the frictional force. The work done by friction is W_f = F_f · x · (). Since the frictional force opposes the motion, the angle between the force and displacement x is 180^, so (180^) = -1. W_f = -F_f · x W_f = -(7700 N) · x Step 4: Apply the work-energy theorem to find the stopping distance x. W_net = KE_f - KE_i -F_f · x = 0 - KE_i -(7700 N) · x = -114978.5 J (7700 N) · x = 114978.5 J x = 114978.5 J7700 N x = 14.9322727... m Step 5: Round the answer to two decimal places as instructed. x ≈ 14.93 m The stopping distance of the car is: 14.93 m Just one more to go today! Send it over.