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QNEET-2024-Ph-62: NEET 2024 Physics - Class 11 NEET-2024-Ph-62 Solution: At any instant of time t the displacement of any particle is…

At any instant of time t the displacement of any particle is given by 2t−12t - 1 (SI unit) under the influence of force of 5 N. The value of instantaneous power is (in SI unit): 10 5 7 6

Multiple Choice Options

  • A 10
  • B 5
  • C 7
  • D 6

Step-by-Step Verified Solution

Core Concept & Governing Formula(s): Instantaneous power delivered by a force is the scalar product of the force vector and the velocity vector of the particle:
P=F⋅vP = \mathbf{F}\cdot\mathbf{v}
When force and motion are along the same line, the vectors can be treated as scalars and the formula reduces to P=F vP = F\,v. Step 1: Determine the velocity of the particle. The displacement is given as a function of time:
x(t)=2t−1 mx(t)=2t-1\ \text{m}
Velocity is the time derivative of displacement:
v(t)=dxdt=ddt(2t−1)=2 m s−1v(t)=\frac{dx}{dt}= \frac{d}{dt}(2t-1)=2\ \text{m s}^{-1}
Thus the particle moves with a constant velocity of 2 m s−12\ \text{m s}^{-1}. Step 2: Use the given constant force. The force acting on the particle is F=5 NF = 5\ \text{N}. Since the direction of the force is along the direction of displacement, we can treat it as a scalar. Step 3: Compute the instantaneous power. Apply P=F vP = F\,v:
P=5 N×2 m s−1=10 WP = 5\ \text{N} \times 2\ \text{m s}^{-1}=10\ \text{W}
Final Conclusion & Correct Option: The instantaneous power at any instant tt is 10 W10\ \text{W}. Correct option: **A) 10**.

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