SSC Selection Post 2025 PYQ — Question 4

Correct Answer

In one-dimensional motion, velocity and acceleration lie along the same line, either in the same or opposite direction.

Explanation

In one-dimensional (1D) motion, an object moves strictly along a straight line (such as along the x-axis). Because the movement is restricted to a single line, any vector quantities like velocity and acceleration can only point forward or backward along that same line. If the object is speeding up, velocity and acceleration point in the same direction. If the object is slowing down (decelerating), acceleration points in the opposite direction to the velocity. Therefore, they always lie along the same line.

The other statements are scientifically incorrect. In one-dimensional motion, velocity and acceleration can never be perpendicular to each other, as perpendicular vectors require at least two dimensions. In two-dimensional (2D) motion, acceleration does not always act opposite to velocity; it can act at any angle relative to the velocity vector (for example, in uniform circular motion, acceleration is always perpendicular to velocity). In three-dimensional (3D) motion, velocity and acceleration are not restricted to the same direction and can have any orientation relative to each other depending on the path of the object.

Key Points

In 1D motion, the direction of the velocity vector determines the direction of motion, while the direction of acceleration relative to velocity determines whether the object speeds up or slows down. When velocity and acceleration have the same sign (same direction), the object speeds up. When they have opposite signs (opposite directions), the object slows down.

Additional Facts

In multi-dimensional motion (2D or 3D), acceleration can be broken down into two components: tangential acceleration and centripetal (or normal) acceleration. Tangential acceleration acts along the line of velocity and changes the object's speed, whereas centripetal acceleration acts perpendicular to the velocity and changes only the direction of motion without altering the speed.

Important Questions and Answers

Question: What is the angle between the velocity vector and acceleration vector for an object thrown vertically upward at the highest point of its trajectory?

Answer: At the highest point, the instantaneous velocity of the object becomes zero, while the acceleration due to gravity still acts vertically downward. Since velocity is zero, the concept of a geometric angle between the two vectors at that exact instant is mathematically undefined.

Question: In uniform circular motion, which is a two-dimensional motion, what is the geometric relationship between velocity and acceleration?

Answer: In uniform circular motion, the acceleration vector (centripetal acceleration) is always perpendicular (90°) to the velocity vector, pointing directly toward the center of the circular path while velocity remains tangential.