A force acts for 10 s on a body of mass 10 kg after which the force ceases and the body describes 50 m in the next 5 s. Find the magnitude of the force.

Answer

To solve the problem step by step, we will follow the reasoning laid out in the video transcript.

### Step 1: Understand the problem
We have a body of mass \( m = 10 \, \text{kg} \) that is acted upon by a force for \( t_1 = 10 \, \text{s} \). After this time, the force ceases, and the body moves a distance of \( d = 50 \, \text{m} \) in the next \( t_2 = 5 \, \text{s} \).

### Step 2: Determine the velocity after the force ceases
When the force stops acting, the body continues to move with a constant velocity. We can calculate this constant velocity \( v \) using the formula:
\[ v = \frac{d}{t_2} \]
Substituting the values:
\[ v = \frac{50 \, \text{m}}{5 \, \text{s}} = 10 \, \text{m/s} \]

### Step 3: Identify the initial and final velocities
Before the force was applied, the body was at rest, so the initial velocity \( u = 0 \, \text{m/s} \). After the force has acted for 10 seconds, the final velocity \( v = 10 \, \text{m/s} \).

### Step 4: Use the equation of motion to find acceleration
We can use the equation of motion:
\[ v = u + at \]
Where:
- \( v \) is the final velocity,
- \( u \) is the initial velocity,
- \( a \) is the acceleration,
- \( t \) is the time duration of the force.

Rearranging this gives us:
\[ a = \frac{v - u}{t_1} \]
Substituting the known values:
\[ a = \frac{10 \, \text{m/s} - 0 \, \text{m/s}}{10 \, \text{s}} = 1 \, \text{m/s}^2 \]

### Step 5: Calculate the force using Newton's second law
According to Newton's second law, the force \( F \) can be calculated as:
\[ F = m \cdot a \]
Substituting the values:
\[ F = 10 \, \text{kg} \cdot 1 \, \text{m/s}^2 = 10 \, \text{N} \]

### Conclusion
The magnitude of the force acting on the body is \( 10 \, \text{N} \).

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