Question

	Column I		Column II
(A)	$\overrightarrow{a}\perp \overrightarrow{v},a\ne 0$	(P)	Speed is constant
(B)	$\overrightarrow{a}\parallel \overrightarrow{v},a\ne 0$	(Q)	Velocity is constant
(C)	$\overrightarrow{a}=0$	(R)	Speed is variable
(D)	$a\ne 0,\overrightarrow{a}$ neither parallel to $\overrightarrow{v}$ nor $\perp \overrightarrow{v}$	(S)	Motion is along a line

Which of the following options has the correct combination considering column-I and column-II ?

• A. B → R, S
• B. A → Q
• C. D → S
• D. C → P, Q

Answer 1

The correct option is A B → R, S

Case (A) : If $\overrightarrow{a}\perp \overrightarrow{v},a\ne 0$

Magnitude of velocity (speed) remains constant but the direction keeps changing. Motion won't be in a straight line.

Case (B) : $\overrightarrow{a}\parallel \overrightarrow{v},a\ne 0$
(A) $\to$ (P)

Magnitude of velocity (speed) keeps changing but the direction remains the same since acceleration is tangential to velocity at each point. Motion will be in a straight line.

(B) $\to$ (R), (S)

Case (C): $\overrightarrow{a}=0$
Neither magnitude nor direction of velocity change and object keeps moving in a straight line with initial velocity.

(C) $\to$ (P), (Q), (S)

Case (D): $a\ne 0,\overrightarrow{a}$ neither parallel to $\overrightarrow{v}$ nor $\perp \text{to}\overrightarrow{v}$

In this case, both magnitude and direction of velocity keep changing and object won't move in a straight line.

(D) $\to$ (R)