Accerlation velosity distance question help not sure if im doing it right?

Question

the acceleration of a particle is directly proportional to the time t.at t =0 velocity =400mm/s.
knowing that at t=1 velocity =370mm/s and distance = 500mm
determine the velocity, the position and the total distance traveled when t = 7s

im not sure if what i have done is correct, i got -60 as the constant which gave velocity at 7s = -1070

can anyone please help?

Answer 1

a=k*t

integrate to get
v=.5*k*t^2+C
C=v0

at t=0 v=400
so v0=400

since at t=1 v=370 mm/s

370=.5*k+400
k=-60


integrate again to get
s=400*t-60*t^3/6+s0

and at t=1 s=500

500=400-60/6+s0
s0=110

so
v(t)=400-30*t^2
v(7)=400-30*49
v(7)=-10170 mm/s

s(t)=130+400*t-10*t^3
s(7)=-500 mm