A particle moving on the positive $x-$axis has a velocity given by $v=\frac{c}{x+1}$ where $v$ is the

velocity in $f\frac{t}{sec,x}$ is the position in ft $,$ and $c$ is a constant to be determined. The particle

starts from the origin $(x=0)$ with an initial velocity $v_0=30f\frac{t}{sec}.(20$ points$)$

a$)$ Determine the constant $c.$

b$)$ Determine the acceleration of the particle at $x=20ft.$

c$)$ Determine the travel time from the origin to the position $x=20ft.$