Question:
The velocity-displacement graph describing the motion of bicycle is shown in the figure.
The acceleration-displacement graph of the bicycle's motion is best described by :
The velocity-displacement graph describing the motion of bicycle is shown in the figure.
The acceleration-displacement graph of the bicycle's motion is best described by :
The acceleration-displacement graph of the bicycle's motion is best described by :
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Use \(a = \frac{dv}{dt} = v\frac{dv}{dx}\); v is linear in x up to 200 m and constant afterwards.
Updated On: Nov 4, 2026
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The Correct Option is A
Solution and Explanation
From the graph, v rises linearly with x from 10 m/s at x = 0 to 50 m/s at x = 200 m, then stays constant up to 400 m.
For 0 to 200 m: \(v = 10 + kx\) with \(k = \frac{dv}{dx} = \frac{40}{200} = 0.2\ \mathrm{s^{-1}}\). Acceleration \(a = v\frac{dv}{dx} = k(10 + kx) = 2 + 0.04x\): a straight line in the a-x graph, starting at 2 m/s2 at x = 0 and increasing linearly.
For 200 to 400 m: v is constant, so \(a = 0\).
So the a-x graph is an inclined straight line starting at 2 on the a-axis up to x = 200 m, followed by a = 0 from 200 m to 400 m. This is option (1).
Answer: (1)
For 0 to 200 m: \(v = 10 + kx\) with \(k = \frac{dv}{dx} = \frac{40}{200} = 0.2\ \mathrm{s^{-1}}\). Acceleration \(a = v\frac{dv}{dx} = k(10 + kx) = 2 + 0.04x\): a straight line in the a-x graph, starting at 2 m/s2 at x = 0 and increasing linearly.
For 200 to 400 m: v is constant, so \(a = 0\).
So the a-x graph is an inclined straight line starting at 2 on the a-axis up to x = 200 m, followed by a = 0 from 200 m to 400 m. This is option (1).
Answer: (1)
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