Velocity-Displacement to Acceleration-Displacement Graph | Motion in 1D | JEE PYQ Solution

 

🚴 Velocity-Displacement Graph of a Bicycle | Find the Acceleration-Displacement Graph | Motion in 1D – Doubtify JEE

📌 Question:

The velocity-displacement graph describing the motion of a bicycle is shown in the figure. What will the corresponding acceleration-displacement graph look like?

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🎯 Concept Tested:

This question tests your graphical understanding of motion — a frequently asked and often misunderstood area in JEE Mains and Advanced. It focuses on converting one type of graph (v-s) into another (a-s) using calculus concepts.

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🔍 How to Approach:

If you're given a velocity-displacement (v-s) graph, and you need to find the acceleration-displacement (a-s) graph, you must apply:

$$a = v \cdot \frac{dv}{ds}$$

This is derived from the chain rule:

$$a = \frac{dv}{dt} = \frac{dv}{ds} \cdot \frac{ds}{dt} = v \cdot \frac{dv}{ds}$$

Depending on the slope of the v-s graph:

• If velocity increases with displacement, acceleration is positive.

• If velocity decreases, acceleration is negative.

• If slope is zero, acceleration is zero.

From the graph in the figure (check the solution link), analyze how v changes with s to derive a vs s.

📷Image Solution:

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📘 Why This Question is Important for JEE:

• Combines graphical interpretation with kinematics equations

• Strengthens visual analysis and mathematical thinking

• These types of questions are regular in JEE Mains PYQs

• Helps students get comfortable with graph-based motion problems

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🧠 Pro Tip by Team Doubtify:

Don’t blindly memorize graph shapes — understand the physics behind each slope and curve. Always relate the physical meaning to mathematical derivatives.

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📹 Watch the Full Explanation:

👉 Stay consistent: Watch – Pause – Understand – Solve

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