A particle moves with a velocity $(5\hat i-3\hat j+6\hat k) ext{ ms}^{-1}$ horizontally under the action of a

Question

A particle moves with a velocity $(5\hat i-3\hat j+6\hat k)	ext{ ms}^{-1}$ horizontally under the action of a constant force $(10\hat i+10\hat j+20\hat k)	ext{ N}$. The instantaneous power supplied to the particle is:

Accepted Answer

1. **Identify the Formula:** The instantaneous power ($P$) is defined as the dot product of the force vector ($\mathbf{F}$) and the velocity vector ($\mathbf{v}$).
   $$ P = \mathbf{F} \cdot \mathbf{v} $$ [Class 11 Physics, Ch 6, Sec 5.10, Eq 5.21]
2. **Substitute Values:**
   $$ \mathbf{F} = 10\hat i + 10\hat j + 20\hat k $$
   $$ \mathbf{v} = 5\hat i - 3\hat j + 6\hat k $$
3. **Calculate Dot Product:**
   $$ P = (10)(5) + (10)(-3) + (20)(6) $$
   $$ P = 50 - 30 + 120 $$
   $$ P = 140	ext{ W} $$

Step-by-Step Solution

Practice All PHYSICS Questions