A force is applied to a 2.04- kg radio-controlled model car parallel to the x-ax

Question

A force is applied to a 2.04- kg radio-controlled model car parallel to the x-axis as it moves along a straight track. The x-component of the force varies with the x-coordinate of the car as shown in figure .Suppose the model car is initially at rest at x=0 and F is the net force acting on it.
http://session.masteringphysics.com/problemAsset/1000062453/4/YF-06-32.jpg

A) What is the work done by the force when the car moves from x = 0 m to x = 3 m?
B) Use the work-energy theorem to find the speed of the car at x=3.0{ m{ m}}.
C) What is the work done by the force on the car from x = 3 m to x = 4 m?
D) Use the work-energy theorem to find the speed of the car at x=4.0m.
E) Use the work-energy theorem to find the speed of the car at x=7.0m.
F) If the initial velocity of our car was 4.7 m/s, what would be the final speed of the car at x = 3 m?

Explanation / Answer

Work done is area under the F-s curve A) 4J B) Kinetic Energy (KE) = Work done, hence v = 1.98m/s C) 0J, area under curve is 0! D) No work done so no increment in KE after x=3m hence v= 1.98m/s E) x=4 to x=6, work is done against KE, hence final KE = 3J. v=1.715m/s. F) Initial KE + Work done = final KE. Hence v = 5.1m/s

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