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

To solve this problem, we need to determine the instantaneous power given the displacement function of a particle and the constant force applied.

Displacement Function: \( x(t) = 2t - 1 \)

Force: \( F = 5 \, \text{N} \)

1. Velocity Calculation: The instantaneous velocity \( v(t) \) is the derivative of the displacement function \( x(t) \) with respect to time \( t \).

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

2. Power Calculation: Instantaneous power \( P \) is given by the product of force and instantaneous velocity.

\( P = F \times v(t) \)

Substituting the given values:

\( P = 5 \, \text{N} \times 2 \, \text{m/s} = 10 \, \text{W} \)

Thus, the value of instantaneous power is 10 W.