A wheeled cart, which is free to move along the x-axis, passes through the origi

Question

A wheeled cart, which is free to move along the x-axis, passes through the origin, moving in the +x direction, with a kinetic energy of 12.0 J. The cart's mass is 5.50 kg. As the graph in the figure below shows, if the cart is between x = ?1 m and x = +2 m, the net force acting on it is 1.00 N in the positive x-direction. If the cart is between x = +2 m and x = +7 m, the net force acting on it is 4.00 N in the negative x-direction. If the cart is between x = +7 m and x = +8 m, the net force acting on it is 2.00 N in the positive x-direction. The net force is zero at all other locations.

Where does the cart reverse direction?

If you wanted the cart to reach the x = +8 m mark, what is the minimum kinetic energy the cart should have at x = 0?

Explanation / Answer

The cart reverses direction when W.D by force + K.E = 0.....i.e, 1*2 -4*(x-2) + 6 = 0..... On solving, we get, x = 4 m................If we want the cart to reach +8 mark...the minimum K.E should be such that cart velocity becomes zero at x = +7 m. So, 1*2-4*5 +K.E = 0........We get, K.E = 18 J

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