Instantaneous Power of a Force – Rankers Physics

Power: Practice Problem & Solution

The position of a particle at any time \( t \) is given by \( x = t^2 + 1 \), where \( x \) is in m and \( t \) is in s. If a constant force of 8 N is acting on the particle, then the instantaneous power of the force at \( t = 1\text{ s} \) will be
8 W
16 W
32 W
19 W

Solution Explained:

To solve this problem, we apply the core principles of Power. Understanding the underlying formula is key to arriving at the correct answer below:

The velocity of the particle is \( v = \frac{dx}{dt} = 2t \). At \( t = 1\text{ s} \), \( v = 2\text{ m/s} \). The instantaneous power is \( P = F \cdot v = 8\text{ N} \times 2\text{ m/s} = 16\text{ W} \).

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