here it is given that a=bt
wkt, a=change in velocitychange in time=dvdt
∴dvdt=bt now integrating this we will get v
v=bt22+c
At t=0 s, v=v0, Thus v0=c
∴v=bt22+v0
Now. v=change in positionchange in time=dsdt=bt22+v0
∴ds=(bt22+v0)dt
∴ Integrating the above we get, s=bt36+v0t+c′at t=0, s=0∴c′=0
i.e. s=bt36+v0t