A particle of mass 0.6kg is subjected to a force of F= -kx with k= 15 `Nm^(-1).` What will be its initial acceleration if it is released from a point 20 cm away from the origin ?

Answer

To find the initial acceleration of a particle subjected to a force of \( F = -kx \), we can follow these steps:

### Step 1: Identify the given values
- Mass of the particle, \( m = 0.6 \, \text{kg} \)
- Spring constant, \( k = 15 \, \text{Nm}^{-1} \)
- Initial position from the origin, \( x = 20 \, \text{cm} = 0.2 \, \text{m} \) (conversion from centimeters to meters)

### Step 2: Write the expression for the force
The force acting on the particle is given by:
\[ F = -kx \]
Substituting the values of \( k \) and \( x \):
\[ F = -15 \times 0.2 \]
Calculating this gives:
\[ F = -3 \, \text{N} \]

### Step 3: Use Newton's second law to find acceleration
According to Newton's second law, the force is also given by:
\[ F = ma \]
Where \( a \) is the acceleration. We can set the two expressions for force equal to each other:
\[ -ma = -kx \]
Substituting the values we have:
\[ -0.6a = -3 \]

### Step 4: Solve for acceleration
Now, we can solve for \( a \):
\[ 0.6a = 3 \]
\[ a = \frac{3}{0.6} \]
Calculating this gives:
\[ a = 5 \, \text{m/s}^2 \]

### Step 5: Determine the direction of acceleration
Since the force was negative, indicating that it acts in the opposite direction to the displacement, the acceleration will also be in the opposite direction. Therefore, we can express the acceleration as:
\[ a = -5 \, \text{m/s}^2 \]

### Final Answer
The initial acceleration of the particle is:
\[ \boxed{-5 \, \text{m/s}^2} \]