Question:
A body is moving in a straight line with constant power. The distance moved by the body in time t is proportional to:
A body is moving in a straight line with constant power. The distance moved by the body in time t is proportional to:
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Constant power implies velocity grows as $\sqrt{t}$, so distance grows as $t^{3/2}$.
Updated On: Jun 10, 2026
- $\sqrt{t}$
- $t^2$
- $t^{3/2}$
- $t^{3/4}$
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The Correct Option is C
Solution and Explanation
Step 1: Concept
Power $P = Fv = (ma)v = m(dv/dt)v$. Since power is constant, $m \cdot v \cdot dv = P \cdot dt$.
Step 2: Analysis
Integrate: $\int m v dv = \int P dt \implies \frac{1}{2}mv^2 = Pt \implies v \propto \sqrt{t}$. Since $v = dx/dt$, $dx \propto \sqrt{t} dt \implies x \propto \int t^{1/2} dt \implies x \propto t^{3/2}$.
Step 3: Conclusion
The distance is proportional to $t^{3/2}$.
Final Answer: (C)
Power $P = Fv = (ma)v = m(dv/dt)v$. Since power is constant, $m \cdot v \cdot dv = P \cdot dt$.
Step 2: Analysis
Integrate: $\int m v dv = \int P dt \implies \frac{1}{2}mv^2 = Pt \implies v \propto \sqrt{t}$. Since $v = dx/dt$, $dx \propto \sqrt{t} dt \implies x \propto \int t^{1/2} dt \implies x \propto t^{3/2}$.
Step 3: Conclusion
The distance is proportional to $t^{3/2}$.
Final Answer: (C)
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