In a force of 9 N is acting on a body, then find instataneous power supplied to the body when its velocity is 5m/s in the direction of force

Options

A. 195 watt
B. 45 watt
C. 75 watt
D. 100 watt

Answer

To find the instantaneous power supplied to a body when a force is acting on it, we can use the formula for power in terms of force and velocity. Here’s the step-by-step solution:

### Step 1: Understand the formula for power
The instantaneous power \( P \) supplied to an object can be calculated using the formula:
\[ P = \mathbf{F} \cdot \mathbf{V} \]
where \( \mathbf{F} \) is the force acting on the body, and \( \mathbf{V} \) is the velocity of the body.

### Step 2: Express the dot product
The dot product can also be expressed as:
\[ P = F \cdot V \cdot \cos(\theta) \]
where \( \theta \) is the angle between the force and the velocity vectors.

### Step 3: Identify the values
In this problem:
- The force \( F = 9 \, \text{N} \)
- The velocity \( V = 5 \, \text{m/s} \)
- Since the velocity is in the same direction as the force, the angle \( \theta = 0^\circ \).

### Step 4: Calculate \( \cos(\theta) \)
The cosine of \( 0^\circ \) is:
\[ \cos(0^\circ) = 1 \]

### Step 5: Substitute the values into the power formula
Now we can substitute the values into the power formula:
\[ P = F \cdot V \cdot \cos(0^\circ) = 9 \, \text{N} \cdot 5 \, \text{m/s} \cdot 1 \]

### Step 6: Perform the multiplication
Calculating the above expression gives:
\[ P = 9 \cdot 5 = 45 \, \text{W} \]

### Final Answer
The instantaneous power supplied to the body is:
\[ \boxed{45 \, \text{W}} \]

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