71) This problem asks us to consider the case in which the objects kinetic energy is conserved. The only way an object's kinetic energy can be changed is if its speed is changed. Thus we need to find the answer choice where the force acting on the object does not change its speed.
Choice A: The velocity and force are acting in the same direction, which means the object is speeding up. Since it is speeding up, its kinetic energy will change.
Choice B: The velocity and force are acting in the opposite direction. This means that the object is slowing down, and its kinetic energy will decrease.
Choice C & D: In this choice, the x-component of the force will cause the object to speed up while the y-component of the force will change the direction of the object.
Choice E: In this situation, there is no component of the force acting in the direction of the velocity. There is only a y-component of the force which is acting perpendicular to the velocity. Since it acts perpendicular to the velocity, the object's speed will remain constant. Furthermore, the kinetic energy will remain the same.
Answer: E
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