Constant Power Motion Simulation
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5
10
1
5
10
Time: 0.00 s
Displacement: 0.00 m
Velocity: 0.00 m/s
Observation: The displacement grows proportionally to \( t^{3/2} \) when an object moves under constant power. This matches the theoretical prediction that for constant power \( P \), displacement \( s \propto t^{3/2} \).
Theoretical Background
For a body moving under constant power \( P \):
1. Power \( P = F \cdot v = \) constant
2. Force \( F = m \cdot a \)
3. Combining: \( P = m \cdot a \cdot v \)
4. Since \( a = \frac{dv}{dt} \), we get \( P = m v \frac{dv}{dt} \)
5. Solving the differential equation gives \( v \propto t^{1/2} \)
6. Integrating velocity gives displacement \( s \propto t^{3/2} \)
Thus, the correct answer is (c) \( t^{3/2} \).
