You can also let Matlab do the heavy lifting by creating an anonymous function and using fplot:
a=8.4;
v=58.8;
fun=@(t) 0 + ...
(t<=7).*(0.5*a.*(t.^2)) + ...
(t>7).*(v.*t);
fplot(fun,[0 30])
However, if you want to make the transition smooth, you will have to adjust a or v:
t=7;
[0.5*a.*(t.^2) v.*t]
To make those equal for some value of t, this relation must hold:
0.5*a.*(t.^2)==v.*t
a*t^2=2vt
at=2v
t=2v/a
If you want t=7, that means
7=2v/a ==> v=7a/2 ==> v=29.4
Now lets plot that one instead:
v=29.4;
fun=@(t) 0 + ...
(t<=7).*(0.5*a.*(t.^2)) + ...
(t>7).*(v.*t);
fplot(fun,[0 30])
