Question

A force of $2\hat{i}+3\hat{j}+4\hat{k}$ $N$ acts on a body for $4$ second, produces a displacement of $\left(3\hat{i}+4\hat{j}+5\hat{k}\right)$ $m$. The power used is

• A. 9.5 W
• B. 7.5 W
• C. 6.5 W
• D. 4.5 W

Answer 1

Answer: (A)

9.5 W

Answer 2

The correct option is(A): 9.5 W.
velocity $=\frac{\text{displacement}}{\text{time}}$
$=\frac{3}{4} \hat{i} + \frac{7}{4} \hat{j} + \frac{5}{4} \hat{k}$
$=\frac{3 \hat{i}}+\hat{j}+\frac{5}{4 \hat{k}}$
$P=F \cdot V$
$=(2 \hat{i}+3 \hat{j}+4 \hat{k}) \cdot\left(\frac{3}{4} \hat{i}+\hat{j}+\frac{5}{4} \hat{k}\right)$
$=2 \times \frac{3}{4}+1 \times 3+4 \times \frac{5}{4}$
$=1.5+3+5=9.5\, W$.