A constant force F is applied to a body of mass m that initially is headed east at velocity v₀ until its velocity becomes −v₀.The total time of travel is 2t.The total distance the body travels in that time is A) . B) . C) . D) . E) .

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The initial velocity of the body is v₀ and the final velocity is −v₀, which means that the velocity has changed by a total of 2v₀. Since a constant force F is applied to the body, we can use the equation F = ma to determine the acceleration, which is a constant throughout the motion. a = F/m Using the kinematic equation v^2 = u^2 + 2as, where u is the initial velocity, v is the final velocity, and s is the distance traveled, we can solve for s: s = (v^2 - u^2)/2a Substituting the values we have, we get: s = ((-v₀)^2 - (v₀)^2)/(2(F/m)) = (2v₀^2)/(2F/m) = (m*v₀^2)/F Since the time of travel is 2t, we know that the average velocity is zero: 0 = (v - u)/2 v = -u Therefore, s = (m*v₀^2)/F = (m*u^2)/F = (m*(v₀^2))/F = (m*(10)^2)/F = 100m/F Therefore, the total distance traveled is proportional to the magnitude of the force F and inversely proportional to the mass of the body m. Out of the given options, B is the only one that matches this result: B) 11ea7ff9_2a84_50c4_a768_9db6990040b0_TB2295_11.

A Constant Force F Is Applied to a Body of Mass