$*5.$ A particle has the following position vector as a function of time:

vec$(r)=r(t)(costhat()+sinthat())$

where $r(t)=r_0{e}^{\frac{t}{T}}.r_0,T,$ and $$ are constants with units of meters, seconds, and radians per second, respectively.

a$)$ Determine vec$(v{)}_{||}$and $.$

b$)$ Determine vec$(a{)}_{||}$and $.$

c$)$ Qualitatively, what do you think this motion looks like? If you were staring at this particle, what would its path through space look like?