contestada

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.

Respuesta :

acceleration of rocket is given here as

[tex]a_y = 2.60* t[/tex]

now we know that

[tex]\frac{dv}{dt} = 2.60t[/tex]

now integrating both sides

[tex]\int dv = \int 2.60t dt[/tex]

[tex]v = 2.60\frac{t^2}{2}[/tex]

[tex]v = 1.30 t^2[/tex]

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

so here we have

[tex]v = 1.30 * 10^2[/tex]

[tex]v = 130 m/s[/tex]

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

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