Question:
The correct position (x) - time (t) graph for a particle moving with negative acceleration is:
The correct position (x) - time (t) graph for a particle moving with negative acceleration is:
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For negative acceleration, the \(x-t\) graph is concave downward; slope decreases over time. Always check the derivative to relate slope to velocity.
Updated On: Jul 18, 2026
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The Correct Option is A
Solution and Explanation
Step 1: Understanding negative acceleration.
Negative acceleration (deceleration) means the velocity of the particle decreases over time. If the particle starts with a positive velocity, it slows down as time progresses.
Step 2: Relation between position and velocity.
Velocity is the derivative of position: \(v = \frac{dx}{dt}\). A decreasing velocity implies that the slope of the \(x-t\) graph decreases over time.
Step 3: Shape of the \(x-t\) graph.
- At the start, the slope (velocity) is maximum.
- As the particle decelerates, the slope reduces gradually to zero if the particle stops.
- This produces a concave downward curve (parabola opening downward).
Step 4: Eliminating other options.
- A straight line would imply constant velocity, which is incorrect.
- A concave upward curve would imply increasing velocity, contradicting negative acceleration.
- Any inverted parabola not matching the slope behavior over time is also incorrect.
Step 5: Conclusion.
The correct \(x-t\) graph for a particle under negative acceleration is a downward concave curve, starting steep and flattening as time progresses.
Step 6: Final statement.
Hence, the correct graph is option (1).
Negative acceleration (deceleration) means the velocity of the particle decreases over time. If the particle starts with a positive velocity, it slows down as time progresses.
Step 2: Relation between position and velocity.
Velocity is the derivative of position: \(v = \frac{dx}{dt}\). A decreasing velocity implies that the slope of the \(x-t\) graph decreases over time.
Step 3: Shape of the \(x-t\) graph.
- At the start, the slope (velocity) is maximum.
- As the particle decelerates, the slope reduces gradually to zero if the particle stops.
- This produces a concave downward curve (parabola opening downward).
Step 4: Eliminating other options.
- A straight line would imply constant velocity, which is incorrect.
- A concave upward curve would imply increasing velocity, contradicting negative acceleration.
- Any inverted parabola not matching the slope behavior over time is also incorrect.
Step 5: Conclusion.
The correct \(x-t\) graph for a particle under negative acceleration is a downward concave curve, starting steep and flattening as time progresses.
Step 6: Final statement.
Hence, the correct graph is option (1).
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