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Summary: The initial problem states: Consider a free particle of mass m moving in one space dimension with velocity v0. Its
starting point is at x = x0 = 0 at time t = t0 = 0 and its end point is at x = x1 = v0t1
at time t = t1 > 0. and this info is to do the 3 problems written out.
a) Calculate the action I for this path.
b) Now suppose that the particle has the same initial and final points in space and
time, but now has an initial velocity v1 6= v0 and a nonzero constant acceleration
a. Find a as a function of v1 and give the trajectory x(t). Note that this is still
a free particle with no potential energy, so x(t) will not satisfy the equations of
motion.
c) Find the action I(v1) for this trajectory, Show that dI/dv1 = 0 for the path
which solves the equation of motion. Is this path a maximum, a minimum. or an
inflection point of I(v1)?
starting point is at x = x0 = 0 at time t = t0 = 0 and its end point is at x = x1 = v0t1
at time t = t1 > 0. and this info is to do the 3 problems written out.
a) Calculate the action I for this path.
b) Now suppose that the particle has the same initial and final points in space and
time, but now has an initial velocity v1 6= v0 and a nonzero constant acceleration
a. Find a as a function of v1 and give the trajectory x(t). Note that this is still
a free particle with no potential energy, so x(t) will not satisfy the equations of
motion.
c) Find the action I(v1) for this trajectory, Show that dI/dv1 = 0 for the path
which solves the equation of motion. Is this path a maximum, a minimum. or an
inflection point of I(v1)?