An object is moving with uniform velocity, and a force acts in the opposite direction to stop it. What is the sign of the work done by this force?
Negative, because the force opposes the motion
Work done by a constant force is \(W = Fs\cos\theta\), where \(\theta\) is the angle between the force and the displacement. The sign of the work therefore depends on this angle.
Here the force acts opposite to the direction in which the object moves, so \(\theta = 180^\circ\) and \(\cos 180^\circ = -1\). So \(W = -Fs\), which is negative. The force takes kinetic energy away from the object, which is why it slows down and stops.
Work is not always positive: it is positive when force and displacement are in the same direction, negative when they are opposite, and zero only when there is no displacement or the force is perpendicular to it. The object is displaced while the force acts, so the work is neither zero nor positive.
Hence, Negative, because the force opposes the motion.
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