Final answer:
The provided question asks to calculate the force responsible for a particle's velocity variation with respect to distance, but lacks critical information like the particle's mass and time-velocity relation, which are essential to solve the problem accurately.
Step-by-step explanation:
The question in discussion requires the calculation of the force responsible for the variation in the velocity of a particle with mass. According to the problem, the speed of the particle varies with distance as v = 2d^2. It is given that when d = 1 m, v = 6 m/s. To find the force, we can apply Newton's second law of motion, which states that force (F) equals mass (m) times acceleration (a).
Firstly, we can find the acceleration by taking the derivative of the velocity function with respect to time (a = dv/dt). However, as we don't have a direct function of velocity with respect to time, we need to use the chain rule to find dv/dt (i.e., dv/dt = dv/dd * dd/dt, where dd/dt is the velocity). Secondly, we insert the known values into the derived formula to calculate the acceleration. Finally, we apply Newton's second law, F = m * a, where m is given and a is calculated from the previous step, to determine the force.
However, as per the provided question, some necessary values such as the mass of the particle and the derivative of the velocity function are missing. Without these specific values, it is not possible to provide an accurate calculation of the force. Therefore, the correct answer cannot be determined from the information given.