Question

Which of the following quantities is NOT a vector? (A) Velocity (B) Force (C) Displacement (D) Distance

Short answer

D) Distance

Step-by-step solution

- Understanding Vectors and Scalars

Vectors are quantities that have both magnitude and direction, such as velocity, force, and displacement. Scalars are quantities that have only magnitude without direction, such as distance.

- Analyzing Each Quantity

Evaluate each quantity given:(A) Velocity: has both magnitude and direction (vector).(B) Force: has both magnitude and direction (vector).(C) Displacement: has both magnitude and direction (vector).(D) Distance: has only magnitude (scalar).

- Identify the Non-Vector Quantity

From the analysis, identify the quantity that is a scalar, not a vector. The scalar quantity here is distance.

Key concepts

Vector Quantities

Vector quantities are essential in physics and mathematics because they provide more detailed information about movement and force. A vector is a quantity that possesses both magnitude and direction. Magnitude refers to the size or length of the vector, while direction indicates where the vector is pointing.

Some examples of vector quantities include:

• Velocity: This vector tells us how fast something is moving and in which direction.
• Force: This represents the push or pull on an object and its direction.
• Displacement: This shows the change in an object's position from its starting point in a specific direction.

Understanding vector quantities is crucial for solving problems in physics, engineering, and many other fields.

Scalar Quantities

Scalar quantities are simpler than vectors because they only have magnitude and no direction. Scalars can tell you the amount of something but not where it's going or coming from.

Some common examples of scalar quantities include:

• Distance: This measures how much ground an object has covered, regardless of its starting or ending point.
• Mass: This indicates how much matter is in an object.
• Temperature: This tells you how hot or cold something is but doesn't provide directional information.

Understanding scalar quantities helps simplify many problems, especially when you only need to know the 'how much' and not the 'where'.

Magnitude and Direction

Magnitude and direction are key characteristics that distinguish vector quantities from scalar quantities.

Magnitude: This refers to the size or amount of the quantity. For a vector, magnitude is often a non-negative number that represents the length of the vector. Mathematically, you might see magnitude symbolized as |𝐕|, where 𝐕 is a vector.

Direction: This tells you where the vector is pointing. Direction is crucial for fully understanding a vector, as it gives context to the magnitude. For example, a force of 10 Newtons to the north is different from 10 Newtons to the south.

When representing vectors visually, we use arrows: the length represents the vector's magnitude, and the arrowhead points in the vector's direction. Comprehending both magnitude and direction is necessary for accurately describing vector quantities and solving related problems.