An object is moving with a uniform acceleration which is parallel to its instantaneous direction of motion. Th

Question

An object is moving with a uniform acceleration which is parallel to its instantaneous direction of motion. The displacement (s) – velocity (v) graph of this object is

Accepted Answer

1. **Kinematic Equation:** For an object moving with uniform (constant) acceleration $a$ along a straight line, the relationship between displacement $s$, final velocity $v$, and initial velocity $u$ is given by the third equation of motion: $v^2 = u^2 + 2as$ .
2. **Mathematical Relationship:** Rearranging the equation to solve for displacement $s$, we get $s = \frac{v^2 - u^2}{2a}$. This equation indicates that displacement $s$ is proportional to the square of the velocity ($s \propto v^2$).
3. **Graphical Shape:** A relationship where one variable is proportional to the square of the other ($y \propto x^2$) represents a **parabola**. Therefore, the graph plotting displacement ($s$) against velocity ($v$) will be a parabolic curve.
4. **Conclusion:** The correct graph corresponding to this motion is a parabola. Assuming the option labeled '4.' depicts a parabola (as per standard solutions for this AIIMS PYQ), it is the correct representation.

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