# Which of the following are vectors and which are scalars: distance, mass, time, weight, volume, density, speed, velocity, acceleration, force, temperature and energy?

Dec 30, 2016

See below.

#### Explanation:

Vector quantities have both magnitude and direction.

Scalar quantities have only magnitude.

Distance is a scalar quantity. It refers only to how far an object has traveled. For example, 4 feet is a distance; it gives no information about direction. To say an object traveled 4 feet is somewhat ambiguous. To say the object traveled 4 feet west, for example, would be a displacement, and would then be a vector quantity. It gives a more complete picture of what happened.

Mass is a scalar quantity. Simply put, it refers to how much matter an object is made up of. It has magnitude but gives no indication of direction in any sense. The vector counterpart to mass is weight.

Weight is a vector quantity. Weight is a force, and forces are vectors, i.e. having both magnitude and direction. Perceived weight of an object at rest on earth is given by $W = {\vec{F}}_{g} = m g$, the product of the mass of the object and the free-fall acceleration constant, $g$, or simply equal to the force of gravity acting on the object. The force of gravity acts downward.

Time is a scalar quantity (as far as we are concerned at this level). It gives information about magnitude, i.e. how much time, but no information about direction.

Volume is a scalar quantity. It refers to the amount of space that an object occupies and therefore has magnitude, but gives no information about direction.

Density is a scalar quantity, having only magnitude and giving no information about direction. We can also reason that, because density is equal to mass divided by volume and both mass and volume are scalar quantities, density must also be a scalar quantity.

Speed is a scalar quantity, having only magnitude and giving no information about direction. For example, $40 \frac{m}{s}$ is a speed, it tells us how fast an object is traveling, but nothing abut which direction the object is traveling in. The vector counterpart to speed is velocity.

Velocity is a vector quantity. Velocities have both magnitude and direction. For example, $40 \frac{m}{s}$ NE is a velocity.

Acceleration is a vector quantity. Acceleration has both magnitude and direction. For example, $9.8 \frac{m}{s} ^ 2$ downward or $- 9.8 \frac{m}{s} ^ 2$ vertically is an acceleration.

Force is a vector quantity. Force has both magnitude and direction. Weight is an example of force given above. Another is the force of friction, which has some magnitude and acts in the direction opposite that of motion.

Temperature is a scalar quantity. A measurement of temperature has magnitude, but gives no information about direction.

Energy is a scalar quantity. It gives information about magnitude, e.g. how much energy an object has, but none about direction.

Note that certain quantities which are alone scalars can be represented as vectors when we discuss intervals or how the quantities change (e.g. measure of increase or decrease).