Answer:
45.125 m/s
Explanation:
Acceleration is given by
[tex]a(t)=p-rt[/tex]
[tex]p=19\ m/s^2[/tex]
r = 4 m/s
[tex]r=4\ m/s^3[/tex]
[tex]v(t)=\int a(t)dt=\int (p-rt)dt=pt-r\dfrac{t^2}{2}[/tex]
For maximum velocity
[tex]0=\dfrac{d}{dt}(pt-r\dfrac{t^2}{2})\\\Rightarrow p-rt=0\\\Rightarrow t=\dfrac{p}{r}\\\Rightarrow t=\dfrac{19}{4}\\\Rightarrow t=4.75\ s[/tex]
Maximum velocity
[tex]v_m=pt-r\dfrac{t^2}{2}\\\Rightarrow v_m=19\times 4.75-4\times\dfrac{4.75^2}{2}\\\Rightarrow v_m=45.125\ m/s[/tex]
The maximum velocity of the rocket is 45.125 m/s
