Question

At any instant of time t, the displacement of any particle is given by 2t – 1 (SI unit) under the influence of force of 5N. The value of instantaneous power is (in SI unit):

• A. 10
• B. 5
• C. 7
• D. 6

Answer 1

The Correct Option is A

Step 1: Find Velocity from Displacement 

The displacement is given by:

$$ x = 2t - 1 $$

Velocity \( v \) is obtained by differentiating displacement with respect to time:

$$ v = \frac{dx}{dt} = \frac{d}{dt} (2t - 1) = 2 \text{ m/s} $$

Step 2: Calculate Instantaneous Power

The formula for instantaneous power is:

$$ P = F \cdot v $$

Given:

F = 5 N

v = 2 m/s

Substituting values:

$$ P = 5 \times 2 = 10 \text{ W} $$

Conclusion

The instantaneous power is 10 W.