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## Homework Statement

A physics student launches a model rocket from the ground at t=0. The rocket ascends with a constant vertical acceleration of a1= 2.5m/s^2 until T1= 5.0s, when the acceleration increases to a2= 5.0m/s^2 until T2= 10.0s. When t>T2, the engine shuts down entirely.

(b) What is the velocity of the rocket when it hits the ground?

## Homework Equations

kinematic equations

## The Attempt at a Solution

v(T1)= 0+(2.5)(5)=12.5m/s

v(T2)=12.5+(5)(5)=37.5m/s

xT1=0+0+1/2at^2=1/2(2.5)(5)^2=31.25m

xT2=31.25+12.5(5.0)+(1/2*5*5^2)=156.25m

V^2=37.5^2-2(9.8)(156.25)=-40.5m/s

but the answer is -66.8 m/s

what am i doing wrong?

Thanks for your help!