Following is an alternative version of the code with some fixings:
load mytrafficdata5;
someidmm(Time_t,Distance_n,Velocity_n)
function someidmm(Time_t,Distance_n,Velocity_n)
% y is distance for follower car
% t is time
% Using interpolant for distance and velocity
close all;
time_vector = Time_t;
y0=[2;2];
tspan=[0 100];
vel_vector = Velocity_n;
Dist_vector= Distance_n;
[t,y] = ode45(@idm8,tspan,y0);
plot(t,y(:,2),'b-',time_vector,vel_vector,'r--')
legend('By IDM','Real Velocity')
xlabel('Time')
ylabel('Velocity (m/sec)')
legend('Location','best')
function dydt = idm8(t,y)
dydt= zeros(2,1)
dydt(1)= y(2);
dydt(2)= a*(1 - (y(2)/x0_dot).^delta - (s_star/s).^2);
% parameters
x0_dot =30; % unit is m/sec
delta =4;
a=0.3;
b= 3;
s0=2;
Th=1.5; %time headway=1.5 sec
k = 1/(2*sqrt(a*b));
lc=5;
dist_interp = interp1(time_vector, Dist_vector, t);
vel_interp = interp1(time_vector, vel_vector, t);
xn = dist_interp;
Delta_v = y(2)-vel_interp;
s = xn-y(1) - lc;
s_star = s0 + max(0,y(2)*Th + y(2)*Delta_v*k);
end
end