Answer with Explanation:
By definition of acceleration we have

Given
, using this value in the above equation we get

Upon integrating on both sides we get

'c' is the constant of integration whose value can be found out by putting value of 't' = 0 and noting V =4 m/s
Thus

the value of 'k' can be found by using the fact that at t= 30 seconds velocity = 26 m/s

Hence the velocity as a function of time is given by

By definition of velocity we have

Making use of the obtained velocity function we get

here
is the constant of integration