What is the height of the rocket above the surface of the earth at t= 10 ?

A rocket starts from rest and moves upward from the surface of the earth. For the first 10s of its motion, the vertical acceleration of the rocket is given by ,a_y=(2.80m/s^3)t where the +y-direction is upward.

a)What is the height of the rocket above the surface of the earth at t= 10 ?

b)What is the speed of the rocket when it is 310m above the surface of the earth?

a_y = 2.80*t

then

Vy = 2.80t²/2 = 1.40t²

y = 1.40 t³/3

So

(a) y(10) = 1.40*1000/3 = 467 m

When y = 310 m ,

t³ = 3*310/1.4 = 664 s³

and

t = 8.72 s

Vy = 1.40*8.72² = 106.6 m/s

What is the height of the rocket above the surface of the earth at t = 10.0 s ?