Question

question #2
reference q.46798
can a scalar have units? give an example.

question #3
reference q.46801
which of the following are expressed as vectors? which are scalars?

a. speed

b. velocity

c. energy

d. distance

e. displacement

f. force

g. time

h. mass

i. weight

j. height

Explanation:

Question #2

A scalar is a physical quantity with magnitude only. Scalars can have units as they represent measurable quantities. For example, mass is a scalar with unit kilograms (kg), time has unit seconds (s), temperature has unit Kelvin (K) or Celsius (°C), etc. Another example: the speed of an object (a scalar) can be measured in meters per second ($m/s$). So yes, scalars can have units.

Answer:

Yes, a scalar can have units. Example: Mass (a scalar) has the unit kilogram (kg), or speed (a scalar) has the unit meter per second ($m/s$).

Question #3

To determine if a quantity is a vector or scalar, we use the definitions:

• Scalar: Quantity with magnitude (size) only (no direction).
• Vector: Quantity with both magnitude and direction.

Let’s analyze each option:

• a. Speed: Magnitude of velocity (no direction) → Scalar.
• b. Velocity: Magnitude + direction (e.g., 5 m/s east) → Vector.
• c. Energy: Magnitude (e.g., 10 J) → Scalar.
• d. Distance: Magnitude of path (no direction) → Scalar.
• e. Displacement: Magnitude + direction (e.g., 3 m north) → Vector.
• f. Force: Magnitude + direction (e.g., 10 N upward) → Vector.
• g. Time: Magnitude (e.g., 5 s) → Scalar.
• h. Mass: Magnitude (e.g., 2 kg) → Scalar.
• i. Weight: Force due to gravity (magnitude + direction, e.g., 98 N downward) → Vector.
• j. Height: Magnitude (e.g., 10 m) → Scalar.