A body of mass m kg starts from rest and travels a distance of s m in t seconds. The force acting on it is

Options

A. `(2 ms )/t^2 N`
B. `(ms)/t N`
C. `(ms^2)/(2t) N`
D. `(ms^2)/t N`

Explanation

To solve the problem of finding the force acting on a body of mass \( m \) kg that starts from rest and travels a distance of \( s \) meters in \( t \) seconds, we can follow these steps:

### Step 1: Identify the given data
- Mass of the body, \( m \) kg
- Distance traveled, \( s \) meters
- Time taken, \( t \) seconds
- Initial velocity, \( u = 0 \) (since the body starts from rest)

### Step 2: Use the kinematic equation
We will use the kinematic equation for uniformly accelerated motion:
\[ s = ut + \frac{1}{2} a t^2 \]
Since the initial velocity \( u = 0 \), the equation simplifies to:
\[ s = \frac{1}{2} a t^2 \]

### Step 3: Solve for acceleration \( a \)
Rearranging the equation to solve for acceleration \( a \):
\[ s = \frac{1}{2} a t^2 \implies a = \frac{2s}{t^2} \]

### Step 4: Apply Newton's second law
According to Newton's second law of motion, the net force \( F \) acting on the body is given by:
\[ F = m \cdot a \]
Substituting the expression for acceleration \( a \):
\[ F = m \cdot \left(\frac{2s}{t^2}\right) \]

### Step 5: Final expression for force
Thus, the force acting on the body can be expressed as:
\[ F = \frac{2ms}{t^2} \]

### Conclusion
The force acting on the body is \( \frac{2ms}{t^2} \) Newtons.

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