Correct Answer Explanation

The correct answer is (C) parabola. A particle starting from rest under constant force experiences constant acceleration, resulting in a quadratic distance-time relationship that plots as a parabola.

Kinematics Equation

Constant force \( F \) produces constant acceleration \( a = \frac{F}{m} \) (Newton’s second law). With initial velocity \( u = 0 \), distance \( s = \frac{1}{2}at^2 \). This quadratic equation \( s \propto t^2 \) yields a parabolic curve on a distance (y-axis) vs. time (x-axis) graph.

Option Analysis

• (A) Straight line: Indicates constant speed (\( s = vt \)), not acceleration from rest.
• (B) Circle: Represents closed periodic motion (e.g., uniform circular), irrelevant for linear force direction.
• (C) Parabola: Matches \( s = \frac{1}{2}at^2 \); velocity-time is linear, integrating to parabola.
• (D) Ellipse: Applies to orbital paths, not straight-line constant force motion.

Graph Derivation

Velocity builds linearly: \( v = at \). Distance integrates velocity: \( s = \int v \, dt = \frac{1}{2}at^2 \). Quadratic form confirms parabola, steeper with time as speed rises.

Common Misconceptions

Straight lines suggest uniform motion, absent here. Circles/ellipses suit 2D orbits, not 1D force along a line.

Exam Relevance

CSIR NET-style MCQs test this: options distinguish constant speed (line) from acceleration (parabola).