We were given a study guide with the answers only to reviewfor our final. Here i

Question

We were given a study guide with the answers only to reviewfor our final. Here is the Problem: A 2.0kg body moving slong the x-axis has a velocity Vx = 5.0m/s at x = 0. The only force acting on the object is given by Fx =(-4.0x)N where x is in m (meters). For what value of x will thisobject first come (momentarily) to a rest? The ans. is 3.5m I tried using the work kinetic energy theorm where W =k Work = f*d = (-4.0x)      k = Kf-Ki, and since the object is comming to rest, Vf =0, so Kf = 0. I come up with -(1/2)(2.0kg)(5.0m/s)^2 = (-4.0x) solving for x I get 6.25m, and the answer is 3.5m. Can anyone give me a hint about this problem? Thanks Everyone! We were given a study guide with the answers only to reviewfor our final. Here is the Problem: A 2.0kg body moving slong the x-axis has a velocity Vx = 5.0m/s at x = 0. The only force acting on the object is given by Fx =(-4.0x)N where x is in m (meters). For what value of x will thisobject first come (momentarily) to a rest? The ans. is 3.5m I tried using the work kinetic energy theorm where W =k Work = f*d = (-4.0x)      k = Kf-Ki, and since the object is comming to rest, Vf =0, so Kf = 0. I come up with -(1/2)(2.0kg)(5.0m/s)^2 = (-4.0x) solving for x I get 6.25m, and the answer is 3.5m. Can anyone give me a hint about this problem? Thanks Everyone!

Explanation / Answer

mass of body m = 2.0 kg initial speed Vx = 5.0 m/s at x = 0 force acting on the object is F = (-4.0x) N x is in meters or m * a = (-4.0x) a is acceleration of body or a = (-4.0x/m) = (-4.0x/2.0) = -2.0x We know from the relation V^2 - Vx^2 = 2ax V is final speed of the body and is equal to zero or (0)^2 - (5.0)^2 = 2 * -2.0x * x or 4.0x^2 = 25 or x = (25/4)^(1/2) = (5/2) = 2.5 m

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