Question:
The graph which cannot possibly represent one-dimensional motion is
The graph which cannot possibly represent one-dimensional motion is
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$x$ vs $t$ graph must always be a function → no loops allowed.
Updated On: May 2, 2026
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The Correct Option is C
Solution and Explanation
Concept: One-dimensional motion and functional requirement
In one-dimensional motion, position must be a function of time: \[ x = f(t) \] This implies:
• For every value of time, there must be only one position
• Graph must satisfy vertical line test
Step 1: Physical meaning of graph
• Time is independent variable
• Position (or velocity/acceleration) depends on time
Step 2: Check each option conceptually
• (A): Acceleration vs time → valid
• (B): Velocity vs time → valid straight-line motion
• (D): Position vs time → oscillatory but single-valued → valid
• (E): Position vs time → piecewise motion → valid
Step 3: Analyze option (C)
• Closed loop (ellipse-like graph)
• At same time → multiple positions
Step 4: Apply vertical line test
• Draw vertical line → intersects graph at multiple points
• Hence not a function
Step 5: Physical contradiction
• Particle cannot be at two positions simultaneously
• Violates fundamental definition of motion Final Answer: \[ \boxed{\text{(C)}} \]
In one-dimensional motion, position must be a function of time: \[ x = f(t) \] This implies:
• For every value of time, there must be only one position
• Graph must satisfy vertical line test
Step 1: Physical meaning of graph
• Time is independent variable
• Position (or velocity/acceleration) depends on time
Step 2: Check each option conceptually
• (A): Acceleration vs time → valid
• (B): Velocity vs time → valid straight-line motion
• (D): Position vs time → oscillatory but single-valued → valid
• (E): Position vs time → piecewise motion → valid
Step 3: Analyze option (C)
• Closed loop (ellipse-like graph)
• At same time → multiple positions
Step 4: Apply vertical line test
• Draw vertical line → intersects graph at multiple points
• Hence not a function
Step 5: Physical contradiction
• Particle cannot be at two positions simultaneously
• Violates fundamental definition of motion Final Answer: \[ \boxed{\text{(C)}} \]
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