Using MATLAB to do Numeric Calculus

So I am culminating all of my newfound knowledge to solve and show a simple calculus problem. However I am running into issues…
Given: A piecewise function where v(t)=70t @ t<=20s & 1596.2-9.81t @ 20<t<t_max <—(eq 1)
Also given: s(t)=35t^2+7620 @ t<=20s & 1596.2t-4.905t^2-8342 @ 20<t<=t_max <—(eq 2)
Find: If aircraft ignites its engines at t=0s and accelerates vertically, there is only enough fuel for an engine burn of 20 seconds. At which time will the ship become a projectile? Find value of t_max. Plot the crafts velocity vs. t, (eq 1). Plot the crafts altitude vs. t, (eq 2).
My Solution:
%% Finding Value of tmax
% Finding tmax and rounding it to the nearest whole number
%%

tmaxr=roots([-9.81, 1596.2]);
tmax=ceil(tmaxr);

%% Plotting Equation 1
% Creating Figure 1 from Equation 1
%%

t=0:0.1:tmax;
v=zeros(size(t));
for N=1:length(t)
if t(N)<=20
v(N)=70*t(N);
else
v(N)=1596.2-9.81*t(N); % Only valid for t > 20 seconds
end
end
figure(1)
plot(t,v)
xlabel(‘Time (s)’)
ylabel(‘Velocity (m/s)’)
title(‘Velocity vs. Time’)

%% Plotting Equation 2
% Creating Figure 2 from Equation 2
%%

t=0:0.1:tmax;
s=zeros(size(t));
for N=1:length(t)
if t(N)<=20
s(N)=35.*t(N).^2+7620;
else
s(N)=1596.2.*t(N)-4.905.*t(N).^2-8342;
end
end
figure(2)
plot(t,s)
xlabel(‘Time (s)’)
ylabel(‘Altitude (m)’)
title(‘Position vs. Time’)
Issue: So I have found t_max, plotted the velocity but it looks funky, and also tried to plot my altitide but not sure if it’s faultless.
P.s. Sorry for the formatting, there’s no easy way to type piecewise functions that I know of.So I am culminating all of my newfound knowledge to solve and show a simple calculus problem. However I am running into issues…
Given: A piecewise function where v(t)=70t @ t<=20s & 1596.2-9.81t @ 20<t<t_max <—(eq 1)
Also given: s(t)=35t^2+7620 @ t<=20s & 1596.2t-4.905t^2-8342 @ 20<t<=t_max <—(eq 2)
Find: If aircraft ignites its engines at t=0s and accelerates vertically, there is only enough fuel for an engine burn of 20 seconds. At which time will the ship become a projectile? Find value of t_max. Plot the crafts velocity vs. t, (eq 1). Plot the crafts altitude vs. t, (eq 2).
My Solution:
%% Finding Value of tmax
% Finding tmax and rounding it to the nearest whole number
%%

tmaxr=roots([-9.81, 1596.2]);
tmax=ceil(tmaxr);

%% Plotting Equation 1
% Creating Figure 1 from Equation 1
%%

%% Plotting Equation 2
% Creating Figure 2 from Equation 2
%%

t=0:0.1:tmax;
s=zeros(size(t));
for N=1:length(t)
if t(N)<=20
s(N)=35.*t(N).^2+7620;
else
s(N)=1596.2.*t(N)-4.905.*t(N).^2-8342;
end
end
figure(2)
plot(t,s)
xlabel(‘Time (s)’)
ylabel(‘Altitude (m)’)
title(‘Position vs. Time’)
Issue: So I have found t_max, plotted the velocity but it looks funky, and also tried to plot my altitide but not sure if it’s faultless.
P.s. Sorry for the formatting, there’s no easy way to type piecewise functions that I know of. So I am culminating all of my newfound knowledge to solve and show a simple calculus problem. However I am running into issues…
Given: A piecewise function where v(t)=70t @ t<=20s & 1596.2-9.81t @ 20<t<t_max <—(eq 1)
Also given: s(t)=35t^2+7620 @ t<=20s & 1596.2t-4.905t^2-8342 @ 20<t<=t_max <—(eq 2)
Find: If aircraft ignites its engines at t=0s and accelerates vertically, there is only enough fuel for an engine burn of 20 seconds. At which time will the ship become a projectile? Find value of t_max. Plot the crafts velocity vs. t, (eq 1). Plot the crafts altitude vs. t, (eq 2).
My Solution:
%% Finding Value of tmax
% Finding tmax and rounding it to the nearest whole number
%%

tmaxr=roots([-9.81, 1596.2]);
tmax=ceil(tmaxr);

%% Plotting Equation 1
% Creating Figure 1 from Equation 1
%%

%% Plotting Equation 2
% Creating Figure 2 from Equation 2
%%

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