Question:
The displacement-time graph of a particle moving along a straight line is shown in the figure. The acceleration-time graph of this particle is:
The displacement-time graph of a particle moving along a straight line is shown in the figure. The acceleration-time graph of this particle is:
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If \(x \propto t^2\), then acceleration is constant.
Updated On: Apr 16, 2026
- Increasing linearly with time
- Constant acceleration
undefined - First increases then decreases
undefined - Increasing non-linearly with time
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The Correct Option is B
Solution and Explanation
Concept:
Acceleration is the second derivative of displacement:
\[
a = \frac{d^2x}{dt^2}
\]
Step 1: Given equation from graph.
From the graph: \[ x = 9t^2 \]
Step 2: Find velocity.
\[ v = \frac{dx}{dt} = 18t \]
Step 3: Find acceleration.
\[ a = \frac{dv}{dt} = 18 \]
Step 4: Conclusion.
Acceleration is constant with time.
Step 1: Given equation from graph.
From the graph: \[ x = 9t^2 \]
Step 2: Find velocity.
\[ v = \frac{dx}{dt} = 18t \]
Step 3: Find acceleration.
\[ a = \frac{dv}{dt} = 18 \]
Step 4: Conclusion.
Acceleration is constant with time.
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