Final answer:
To experimentally test the empirical law F = R/t² v(t), one should plot logv(t) against 1/t², which linearizes the relationship and directly compares the logarithm of the velocity to the inverse square of time.
Step-by-step explanation:
The student's question involves an empirical force law F = R/t² v(t), where R is a constant, t is time, and v(t) is the velocity at time t. To test this law experimentally, one needs to plot a graph that allows the direct measurement of the parameters and constants involved.
Since the force is inversely proportional to the square of time and directly proportional to velocity, we must eliminate the square dependency on time to linearize the relationship for a plot.
Plotting logv(t) against 1/t² would linearize the equation since the logarithm of velocity logv(t) should be directly proportional to 1/t².
Therefore, option C is the most suitable choice.