$1-(10$ Points$)$ A $0\mathrm{.}100-kg$ toy car is propelled by a compressed spring. The car follows a track that rises $0\mathrm{.}180$ m above the starting point. The spring is compressed $4\mathrm{.}00$ cm and has a force constant of $250\mathrm{.}0\frac{N}{m}.$ Assuming work done by friction to be negligible, find:

a$.(4$ Points$)$ The spring Potential Energy before and after release?

b$.(3$ Points$)$ How fast is the car going before it starts up the slope?

c$.(3$ Points$)$ How fast is it going at the top of the slope?

d$.(5$ Bonus$)$ Knowing how fast the car is going from part $($b$),$ if the spring was intact with the car for $0\mathrm{.}5$ s $,$ find the car average acceleration.