The brakes of a truck cause it to slow down by applying a...

The brakes of a truck cause it to slow down by applying a retarding force of $3.0 \times 10^{3} \mathrm{N}$ to the truck over a distance of $850 \mathrm{m} .$ What is the work done by this force on the truck? Is the work positive or negative? Why?

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Key Concepts

Negative Work

Negative work occurs when the force applied to an object is directed opposite to the displacement, meaning the cosine of the angle between them is negative. In such cases, the force removes energy from the object, leading to a decrease in its kinetic energy. This concept is crucial in situations where forces, such as friction or braking forces, act to slow down moving objects.

Work

Work in physics is defined as the energy transferred to or from an object through the application of a force along a displacement. The work done by a constant force is calculated as the product of the force magnitude, the displacement magnitude, and the cosine of the angle between the force vector and the displacement vector. It is measured in joules (J) and is a scalar quantity.

Dot Product

The dot product is a mathematical operation used in the calculation of work. It combines two vectors—the force and the displacement—by multiplying their magnitudes and the cosine of the angle between them. This operation determines whether the force contributes to increasing or decreasing the object's energy based on its direction relative to the displacement.

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