At any instant of time $t$, the displacement of any particle is given by $2t-1$ (SI unit) under the influence

Question

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

Accepted Answer

1. **Identify the Formula:** Instantaneous power ($P$) is defined as the product of the force ($F$) and the instantaneous velocity ($v$).
   $$ P = Fv $$ [Class 11 Physics, Ch 6, Sec 6.10, Eq 6.21]
2. **Calculate Velocity:** Velocity is the time derivative of displacement ($x$).
   Given displacement $x = 2t - 1$.
   $$ v = \frac{dx}{dt} = \frac{d}{dt}(2t - 1) = 2 	ext{ m/s} $$ [Class 11 Physics, Ch 3, Sec 3.2, Eq 3.1b]
3. **Calculate Power:**
   Given Force $F = 5 	ext{ N}$.
   $$ P = 5 	ext{ N} 	imes 2 	ext{ m/s} = 10 	ext{ W} $$

Step-by-Step Solution

Practice All PHYSICS Questions