A body in motion continues in motion with the same speed and in the same direction unless acted upon by an unbalanced force.” Newton’s first law states that: “A body at rest will remain at rest unless acted on by an unbalanced force. Source: University Physics Volume 1, OpenStax CNX The operation of division by a vector is not defined. We can add or subtract two vectors, and we can multiply a vector by a scalar or by another vector, but we cannot divide by a vector. In the language of mathematics, physical vector quantities are represented by mathematical objects called vectors. Examples of vector quantities include displacement, velocity, position, force, and torque. Physical quantities specified completely by giving a number of units (magnitude) and a direction are called vector quantities. Coast Guard dispatches a ship or a helicopter for a rescue mission, the rescue team must know not only the distance to the distress signal, but also the direction from which the signal is coming so they can get to its origin as quickly as possible. Many physical quantities, however, cannot be described completely by just a single number of physical units. For example, if a train covers a distance of 100 km in 1.0 h, its speed is 100.0 km/1.0 h = 27.8 m/s, where the speed is a derived scalar quantity obtained by dividing distance by time. Two scalar quantities can also be multiplied or divided by each other to form a derived scalar quantity. For example, if yesterday’s breakfast had 200 cal of energy and today’s breakfast has four times as much energy as it had yesterday, then today’s breakfast has 4(200 cal) = 800 cal of energy. When we multiply a scalar quantity by a number, we obtain the same scalar quantity but with a larger (or smaller) value. Similarly, a 60-cal serving of corn followed by a 200-cal serving of donuts gives (60 cal + 200 cal) = 260 cal of energy. For example, a class ending 10 min earlier than 50 min lasts (50 min – 10 min) = 40 min. Scalar quantities that have the same physical units can be added or subtracted according to the usual rules of algebra for numbers. Scalar is a synonym of “number.” Time, mass, distance, length, volume, temperature, and energy are examples of scalar quantities. For example, “a class period lasts 50 min” or “the gas tank in my car holds 65 L” or “the distance between two posts is 100 m.” A physical quantity that can be specified completely in this manner is called a scalar quantity.

Many familiar physical quantities can be specified completely by giving a single number and the appropriate unit.

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