Match each physical scenario or vector operation on the left with its corresponding physic… — JAMB UTME

Match each physical scenario or vector operation on the left with its corresponding physical property or resultant classification on the right.

A particle moving in a circular path at a constant speed of $10\text{ m s}^{-1}$ A vector quantity of constant magnitude but continuously changing direction
The dot (scalar) product of force and displacement vectorsA scalar quantity representing work done
Two forces of equal magnitude $P$ acting on a point at an angle of $120^\circ$ to each otherA single resultant vector of magnitude equal to $P$
The slope of a displacement-time graphA vector quantity representing velocity

Answer

Particle in uniform circular motion pairs with a vector quantity of constant magnitude but changing direction; Dot product of force and displacement pairs with a scalar quantity representing work done; Two equal forces at 120 degrees pair with a resultant magnitude equal to P; Slope of displacement-time graph pairs with a vector quantity representing velocity.

Each physical scenario correctly corresponds to its fundamental vector/scalar classification or calculated resultant based on vector algebra.

Step-by-Step Solution

Analyze circular motion at constant speed

The velocity vector changes direction at every point, giving rise to centripetal acceleration directed toward the center.

Any physical quantity with direction is a vector quantity.

Evaluate the product of force and displacement vectors

W = \mathbf{F} \cdot \mathbf{d} = F d \cos\theta

, producing a scalar quantity (work done).

The dot product of two vectors yields a scalar.

Calculate the resultant of two equal vectors

P

120^\circ

R = \sqrt{P^2 + P^2 + 2P^2 \cos 120^\circ} = \sqrt{2P^2 - P^2} = P

Vector addition follows the law of cosines taking spatial angle into account.

Determine the physical quantity represented by the gradient of a displacement-time graph

\text{Slope} = \frac{\Delta s}{\Delta t} = v \text{ (velocity)}.

Displacement per unit time is velocity, a vector quantity.

Key Concept

Scalars, Vectors, and Vector Addition Laws

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