Question 82 of 308

The velocity $(v)$ - Distance $(x)$ graph is shown in figure. Which graph represents acceleration $(a)$ versus distance $(x)$ variation of this system?

ABCD

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Answer: (A)

The v-x graph shows velocity decreasing linearly with distance. Using kinematic equation $v^2 = v_0^2 + 2ax$, we can establish the relationship between acceleration and position.
From the linear v-x relationship, differentiating using $a = v\frac{dv}{dx}$ yields acceleration that is linearly proportional to distance from the origin.
The a-x graph shows a straight line passing through the origin with positive slope, indicating that acceleration increases linearly with distance while remaining positive throughout the motion.

JEE Main Physics practice question on Kinematics (Graphs of motion in one dimension), with the answer and a step-by-step solution. Scan a question from your own book or paper to get a whiteboard video.