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A car drives 200 m north, then 150 m south. Determine the distance traveled and the displacement of the car. State the direction of the displacement.
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Finding the distance traveled $$d=200+150=350\text{ m}$$ Finding the displacement (taking north as positive) $$s=(+200)+(-150)=+50\text{ m}$$ The distance traveled is 350 m and the displacement is 50 m north.
Indicate whether speed can ever be negative? Justify your response.
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Speed cannot be negative because speed is a scalar quantity defined as the magnitude of velocity. Magnitude is always zero or positive, so speed has no directional sign.
Two forces act on a block along the same line. Force $\vec{A}$ is 8 N to the right and force $\vec{B}$ is 12 N to the left. Determine the magnitude and direction of the vector sum of these two forces.
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Taking rightward as positive, the components are +8 N and −12 N. Finding the vector sum $${F}_{\text{net}}=(+8)+(-12)=-4\text{ N}$$ The negative sign means the resultant force is 4 N to the left.
Indicate whether displacement can be zero when distance is nonzero? Justify your response using the definitions of these two quantities.
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Displacement can be zero when distance is nonzero. Displacement depends only on the initial and final positions, so if an object returns to its starting point, the change in position is zero. Distance, however, accumulates every meter of path traveled, so it remains positive for any object that has moved at all.