A constant retarding force of 50N is allied to a body of mass 10kg moving initially with a speed of `10ms^(-1)` . The body comes to rest after

Options

A. 2s
B. 4s
C. 6s
D. 8s

Explanation

To solve the problem step by step, we will follow the principles of Newton's laws of motion and the equations of motion.

### Step 1: Identify the given values
- Mass of the body (m) = 10 kg
- Initial speed (u) = 10 m/s
- Final speed (v) = 0 m/s (since the body comes to rest)
- Retarding force (F) = -50 N (negative because it is a retarding force)

### Step 2: Calculate the acceleration
Using Newton's second law of motion, we know that:
\[ F = m \cdot a \]
Where:
- \( F \) is the force applied (in this case, the retarding force),
- \( m \) is the mass of the body,
- \( a \) is the acceleration.

Rearranging the formula to find acceleration:
\[ a = \frac{F}{m} \]

Substituting the values:
\[ a = \frac{-50 \, \text{N}}{10 \, \text{kg}} = -5 \, \text{m/s}^2 \]

### Step 3: Use the equation of motion to find time
We can use the first equation of motion:
\[ v = u + a \cdot t \]

Substituting the known values:
- \( v = 0 \, \text{m/s} \)
- \( u = 10 \, \text{m/s} \)
- \( a = -5 \, \text{m/s}^2 \)

Now, substituting these values into the equation:
\[ 0 = 10 + (-5) \cdot t \]

Rearranging the equation to solve for \( t \):
\[ -10 = -5t \]
\[ t = \frac{10}{5} = 2 \, \text{s} \]

### Conclusion
The body comes to rest after **2 seconds**.

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