A

To find the work done by the force on the particle as it moves from x = 0 to x = 5 m, we need to calculate the work done using the formula:
Work (W) = \int_{x_1}^{x_2} F(x) \, dx
Here, F(x) = 3x^2 - 2x + 7, x_1 = 0, and x_2 = 5.
Step 1: Set up the integral:
W = \int_{0}^{5} (3x^2 - 2x + 7) \, dx
Step 2: Calculate the integral:
\int (3x^2) \, dx = x^3, \int (-2x) \, dx = -x^2, \int (7) \, dx = 7x
Therefore,
W = \left[ x^3 - x^2 + 7x \right]_{0}^{5}
Step 3: Evaluate the definite integral:
W = \left[ 5^3 - 5^2 + 7(5) \right] - \left[ 0^3 - 0^2 + 7(0) \right]
W = (125 - 25 + 35) - 0 = 135 J
Therefore, the work done by the force is 135 J.