Question

Velocity of particle varies with position as shown in figure. Find the correct variation of acceleration with position. 

• A. A
• B. B
• C. C
• D. D

Hint:

When velocity is given as function of position, use $a = v \dfrac{dv}{dx}$.

Answer 1

The Correct Option is D

Step 1: Use the relation between acceleration, velocity, and position

When velocity v is a function of position x, acceleration is given by:

a = v (dv/dx)

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Step 2: Interpret the given v–x graph

From the velocity versus position graph, velocity decreases linearly with position.

Hence, velocity can be written as:

v = −kx + c

where k and c are positive constants.

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Step 3: Differentiate velocity with respect to position

dv/dx = −k

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Step 4: Find acceleration as a function of position

a = v (dv/dx)

a = (−kx + c)(−k)

a = k²x − kc

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Step 5: Analyze the nature of the a–x graph

The expression a = k²x − kc represents a straight line:

• Slope = k² (positive)
• Intercept = −kc (negative)

Thus, acceleration varies linearly with position and increases with x, starting from a negative value at x = 0.

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Final Answer:

The correct acceleration versus position graph is a straight line with positive slope, corresponding to
Option D