A body of mass 2 kg is at rest. Two forces of 6 N and 8 N act on the body at right angles to each other. What is the velocity of the body after 3 second?

Options

A. 10m/s
B. 15m/s
C. 5m/s
D. 20m/s

Explanation

To solve the problem step by step, we will follow the physics principles of force, acceleration, and motion.

### Step 1: Determine the Resultant Force
Given two forces acting at right angles to each other, we can find the resultant force using the Pythagorean theorem.

1. **Force 1 (F1)** = 6 N
2. **Force 2 (F2)** = 8 N

The magnitude of the resultant force (F) can be calculated as:
\[ F = \sqrt{F_1^2 + F_2^2} \]
Substituting the values:
\[ F = \sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10 \text{ N} \]

### Step 2: Calculate the Acceleration
Using Newton's second law of motion, we can find the acceleration (a) of the body. The formula is:
\[ F = m \cdot a \]
Where:
- \( F \) is the resultant force (10 N)
- \( m \) is the mass of the body (2 kg)

Rearranging the formula to find acceleration:
\[ a = \frac{F}{m} = \frac{10 \text{ N}}{2 \text{ kg}} = 5 \text{ m/s}^2 \]

### Step 3: Use the First Equation of Motion to Find Final Velocity
Now, we will use the first equation of motion to find the final velocity (v) after a time (t) of 3 seconds. The equation is:
\[ v = u + a \cdot t \]
Where:
- \( u \) is the initial velocity (0 m/s, since the body is at rest)
- \( a \) is the acceleration (5 m/s²)
- \( t \) is the time (3 s)

Substituting the values:
\[ v = 0 + (5 \text{ m/s}^2) \cdot (3 \text{ s}) = 15 \text{ m/s} \]

### Final Answer
The velocity of the body after 3 seconds is **15 m/s**.

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