A constant force acts on a body of mass 0.9 kg at rest for 10 s . If the body moves a distance of 250 m, the magnitude of the force is

Options

A. `3N`
B. `3.5 N`
C. `4.0N`
D. `4.5N`

Answer

To find the magnitude of the force acting on a body of mass 0.9 kg that moves a distance of 250 m in 10 seconds, we can follow these steps:

### Step 1: Identify the given values
- Mass of the body (m) = 0.9 kg
- Distance (s) = 250 m
- Time (t) = 10 s
- Initial velocity (u) = 0 m/s (since the body is at rest)

### Step 2: Use the second equation of motion
We can use the second equation of motion, which relates displacement, initial velocity, time, and acceleration:
\[ s = ut + \frac{1}{2} a t^2 \]

### Step 3: Substitute the known values into the equation
Since the initial velocity (u) is 0, the equation simplifies to:
\[ s = \frac{1}{2} a t^2 \]

Substituting the known values:
\[ 250 = \frac{1}{2} a (10)^2 \]

### Step 4: Solve for acceleration (a)
Now, we can solve for acceleration (a):
\[ 250 = \frac{1}{2} a (100) \]
\[ 250 = 50a \]
\[ a = \frac{250}{50} = 5 \, \text{m/s}^2 \]

### Step 5: Calculate the force (F)
Now that we have the acceleration, we can calculate the force using Newton's second law:
\[ F = m \cdot a \]

Substituting the values:
\[ F = 0.9 \, \text{kg} \cdot 5 \, \text{m/s}^2 \]
\[ F = 4.5 \, \text{N} \]

### Conclusion
The magnitude of the force acting on the body is **4.5 Newtons**.

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