A force F is exerted on a body of mass M, which is connected to a spring (spring constant k). The body has a constant acceleration a. Calculate the work done by the external force in moving the body by a distance D.

Explanation

To solve the problem of calculating the work done by the external force in moving a body of mass \( M \) connected to a spring with spring constant \( k \), while the body experiences a constant acceleration \( a \) over a distance \( D \), we can follow these steps:

### Step 1: Understand the Forces Acting on the Body
The external force \( F \) is applied to the body. The body is also subjected to the restoring force of the spring, which is given by Hooke's law as \( F_{spring} = kx \), where \( x \) is the displacement of the spring from its equilibrium position.

### Step 2: Write the Equation of Motion
Using Newton's second law, the net force acting on the body can be expressed as:
\[
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