Answer:
s(t) = (-t^3)/3 + (t^2)/2 + 4t + 7
Step-by-step explanation:
a = -t +1
to find the equation for velocity we need to integrate the acceleration equation,
v = (-t^2)/2 + t + c
c is an arbitrary constant
as it is given v(0) = 4 m/s
4 = 0 + 0 + c
c = 4
now let's integrate again to find the displacement equation,
s = (-t^3)/3 + (t^2)/2 + 4t + c1
c1 is an arbitrary constant
given s(0) = 7m
7 = 0 + 0 + 0 + c1
c1 = 7
so the final answer is,
s(t) = (-t^3)/3 + (t^2)/2 + 4t + 7