code for diagram

> g:=x->a*x^2 +b*x+c:

> fsolve({g(12)=55,g(35)=25,2*a*35+b=0},{a,c,b}):

> g:=x->30/529*x^2 -2100/529*x+49975/529:

> F:=piecewise(x<12,55*sin(x*Pi/24),x<50,g(x)):

> f:=unapply(F,x):

> p1:=plot(f(x),x=0..35,labels=[`time (sec)`,`vel. m/sec`],labelfont=[TIMES,BOLD,14],xtickmarks=[0,5,
10,15,20,25,30,35],ytickmarks=[0,10,20,30,40,50,60],
axesfont=[TIMES,BOLD,14],thickness=2):p1;