The acceleration of an object in the space is given by the vector function below:

 

a (t) = t ² i  + e ^-t j + t k

 

 Find the position vector function, r (t), of this object if the initial velocity is 2 i - j + 3 k and the initial position is j . Then, find the location of the object at the time t = 5 secs and t = 25 secs.