Work And Energy

To calculate the work done, we need to integrate the force over the displacement. Since the velocity is given as a function of , we can find the work done by using the work-energy theorem.

1. Step 1: Calculate the acceleration. The velocity is given by . To find the force, we first need the acceleration, which is the derivative of velocity with respect to time. We use the chain rule: First, calculate the derivative of velocity with respect to :

2. Step 2: Calculate the work done. The work done is the integral of force over displacement. The force is . By substituting the values and integrating over the limits to , we get: After performing the integration, we get the work done as: Thus, the work done is 6.4 J.

Work done by a variable force is: Here, So, So the work done is:
Hence, the correct answer is: