A car (m=1200 kg) is traveling at an initial speed of 15 m /...

A car $(m=1200 \mathrm{kg})$ is traveling at an initial speed of $15 \mathrm{m} / \mathrm{s}$. It then slows to a stop over a distance of $80 \mathrm{m}$ due to a force from the brakes. How much work is done on the car? Assume the
acceleration is constant.

Key Concepts

Work

Work is the process by which energy is transferred by a force acting over a distance. It is calculated as the product of the force applied, the displacement of the object in the direction of the force, and the cosine of the angle between the force and displacement vectors. Work is a scalar quantity measured in joules in the International System of Units.

Kinetic Energy

Kinetic energy is the energy that an object possesses due to its motion. It is given by the formula ½mv², where m is the mass of the object and v is its velocity. Changes in kinetic energy often underlie the analysis of problems involving objects speeding up or slowing down.

Work-Energy Theorem

The work-energy theorem states that the net work done on an object is equal to its change in kinetic energy. This principle provides a powerful tool for analyzing mechanical systems, as it connects the concepts of force, displacement, and energy without requiring detailed information about the forces over time.

Constant Acceleration

Constant acceleration implies that an object’s acceleration remains uniform during the period of motion. This assumption allows the use of kinematic equations to relate displacement, velocity, acceleration, and time. While not directly needed to calculate work, it is often used to further analyze motion dynamics in problems where forces cause objects to speed up or slow down.

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