Question

A rocket starts from rest and moves upward from the surface of the earth. for the first 10.0 s of its motion, the vertical acceleration of the rocket is given by ay=(2.60m/s3)t, where the +y-direction is upward.

Answer 1

acceleration of rocket is given here as

$a_y = 2.60* t$

now we know that

$\frac{dv}{dt} = 2.60t$

now integrating both sides

$\int dv = \int 2.60t dt$

$v = 2.60\frac{t^2}{2}$

$v = 1.30 t^2$

here since its given that rocket will accelerate for t = 10 s

so here we have

$v = 1.30 * 10^2$

$v = 130 m/s$

so after t = 10 s the speed of rocket will be 130 m/s upwards