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
- 9.5 W
- 7.5 W
- 6.5 W
- 4.5 W
The Correct Option is A
Solution and Explanation
velocity \(=\frac{\text{displacement}}{\text{time}}\)
\(=\frac{3}{4} \hat{i} + \frac{7}{4} \hat{j} + \frac{5}{4} \hat{k}\)
\(=\frac{3 \hat{i}}+\hat{j}+\frac{5}{4 \hat{k}}\)
\(P=F \cdot V\)
\(=(2 \hat{i}+3 \hat{j}+4 \hat{k}) \cdot\left(\frac{3}{4} \hat{i}+\hat{j}+\frac{5}{4} \hat{k}\right)\)
\(=2 \times \frac{3}{4}+1 \times 3+4 \times \frac{5}{4}\)
\(=1.5+3+5=9.5\, W\).
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- Solutions
Concepts Used:
Power
Power is the rate of doing an activity or work in the minimum possible time. It is the amount of energy transferred or converted per unit of time where large power means a large amount of work or energy.
For example, when a powerful car accelerates speedily, it does a large amount of work which means it exhausts large amounts of fuel in a short time.
The formula of Power:
Power is defined as the rate at which work is done upon an object. Power is a time-based quantity. Which is related to how fast a job is done. The formula for power is mentioned below.
Power = Work / time
P = W / t
Unit of Power:
As power doesn’t have any direction, it is a scalar quantity. The SI unit of power is Joules per Second (J/s), which is termed as Watt. Watt can be defined as the power needed to do one joule of work in one second.