PROBLEM $1$: A solar sail is propelled by sunlight reflecting from a highly reflective surface. Such a sail is released from rest at a distance of $2\mathrm{.}0$ x $1011$ m from the Sun, where the solar sail experiences a net force of $4\mathrm{.}0$ N$,$ directed away from the Sun. The solar sail has a mass of $4000$ kg$.$ Assume the only forces acting are the force from radiation pressure and the gravitational force from the Sun.

$($a$)$ Calculate the initial acceleration of the solar sail.

$($b$)$ The solar sail travels for $2\mathrm{.}0$ x $107$ s $($about eight months$).$ Assuming constant acceleration,

what is its speed at this time?

$($c$)$ Assuming constant acceleration, how far has the solar sail traveled in this time?

$($d$)$ As time goes by and the solar sail gets farther from the Sun, the solar sail's acceleration

actually $...$

$[]$increases $[]$isconstant $[]$decreases

$($e$)$ During which $4-$month period will the solar sail travel farther, the first four months or the second four months?

$[]$thefirstfourmonths $[]$thesecondfourmonths $[]$neither$$itwillbethesame

Briefly justify your answer: