Answer:
To find the work done in moving the particle from the origin to x = 2, we need to integrate the force over the given interval.
The work done (W) is calculated by integrating the force function with respect to displacement (dx) from the initial position (0) to the final position (2):
W = ∫(0 to 2) (10x³ - 5) dx
Integrating the force function, we get:
W = ∫(0 to 2) (10x³ - 5) dx = [2.5x⁴ - 5x] evaluated from 0 to 2
Now, substituting the upper limit (2) and lower limit (0) into the equation:
W = [2.5(2)⁴ - 5(2)] - [2.5(0)⁴ - 5(0)]
= [2.5(16) - 10] - [0 - 0]
= 40 - 10
= 30
Therefore, the work done in moving the particle from the origin to x = 2 is 30 units of work.
Step-by-step explanation: