MCAT Physical : Scalar and Vector Quantities
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Example Questions
Example Question #1 : Scalar And Vector Quantities
A student measures the mass, volume, weight, and density of a solid in SI units. Which measurement(s) has/have units that are not a type of derived unit?
Mass and weight
Only mass
Weight and density
Mass and volume
Only mass
There are two types of units: base units and derived units. Base units are a set of units from which all other units are derived, whereas derived units are the units derived from base units.
There are six main base units: meters, kilogram, second, Ampere, Kelvin, moles, and candela (unit for luminous intensity). The rest of the units are classified as derived units and will contain a combination of these base units. The SI units for the four measurements listed in question are as follows:
Mass:
Volume: 
Weight: 
Density:
This means that volume, weight, and density are derived units, whereas mass is a base unit.
Example Question #1 : Scalar And Vector Quantities
Which of the following is true about SI derived units and base units?
Units for force can be either derived units or base units
Derived units are obtained by adding, subtracting, multiplying, and/or dividing base units
There are more base units than derived units
Hours are a type of SI base unit
Hours are a type of SI base unit
Derived units are derived from the six base units. A derived unit usually contains multiple base units that are combined by using multiplication and/or division; addition and subtraction of base units is not performed to obtain derived units.
The SI unit for force is Newtons. Newtons written in base units is 
The SI base unit for time is seconds. Hours are derived by multiplying seconds by sixty. Hours are not a base unit.
Example Question #3 : Scalar And Vector Quantities
The unit for mass is a type of __________ unit. The unit "moles" is a type of __________ unit.
derived . . . derived
base . . . base
derived . . . base
base . . . derived
base . . . base
Recall that the mass of a substance is usually measured in kilograms (
Example Question #1 : General Principles
Which answer choice below includes only scalar quantities?
Acceleration, energy, displacement
Force, time, velocity
Velocity, displacement, force
Displacement, time, acceleration
Distance, speed, time
Distance, speed, time
Scalar quantities are those that can be described with magnitude only, as opposed to vectors, which include both magnitude and direction components. Distance, speed, and time are all scalars. Displacement is not a scalar, as it involves both the distance and the direction moved from a starting point. Velocity also includes a direction component, and is therefore a vector quantity.
Example Question #4 : Scalar And Vector Quantities
An airplane is in flight. Which of the following is an example of a vector?
The distance traveled by the plane
The angle at which the plane flies
The velocity of the plane
None of these are vectors
The speed of the plane
The velocity of the plane
A vector quantity has has both magnitude and direction. By definition, only velocity satisfies these criteria.
Distance, angle, and speed have magnitude, but no direction.
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