A force of certain magnitude acts on a body. The mass of the body is 10 kg. The time for which the force acting is 10 s. This force makes the body move at a distance of 50 m in 5 s after the force cease to act on it
What is the magnitude of force applied on the body?

Options

A. 5 N
B. 10 N
C. 15 N
D. 20 N

Explanation

To find the magnitude of the force applied on the body, we can follow these steps:

### Step 1: Understand the given information
- Mass of the body (m) = 10 kg
- Time for which the force acts (t) = 10 s
- Distance moved after the force ceases to act = 50 m
- Time taken to move that distance = 5 s

### Step 2: Calculate the final velocity (v) after the force ceases to act
The final velocity can be calculated using the formula:
\[ v = \frac{\text{distance}}{\text{time}} \]
Substituting the values:
\[ v = \frac{50 \text{ m}}{5 \text{ s}} = 10 \text{ m/s} \]

### Step 3: Use the first equation of motion to find acceleration (a)
The first equation of motion is:
\[ v = u + at \]
Where:
- \( v \) = final velocity = 10 m/s
- \( u \) = initial velocity = 0 m/s (the body starts from rest)
- \( a \) = acceleration
- \( t \) = time = 10 s (the time the force acts)

Rearranging the equation to find acceleration:
\[ 10 \text{ m/s} = 0 + a \times 10 \text{ s} \]
Thus,
\[ a = \frac{10 \text{ m/s}}{10 \text{ s}} = 1 \text{ m/s}^2 \]

### Step 4: Calculate the force (F) using Newton's second law
Newton's second law states:
\[ F = m \times a \]
Substituting the values:
\[ F = 10 \text{ kg} \times 1 \text{ m/s}^2 = 10 \text{ N} \]

### Final Answer
The magnitude of the force applied on the body is **10 Newtons**.

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