To solve this problem it is necessary to apply the kinematic equations of motion.
By definition we know that the position of a body is given by
[tex]x=x_0+v_0t+at^2[/tex]
Where
[tex]x_0 =[/tex] Initial position
[tex]v_0 =[/tex] Initial velocity
a = Acceleration
t= time
And the velocity can be expressed as,
[tex]v_f = v_0 + at[/tex]
Where,
[tex]v_f = Final velocity[/tex]
For our case we have that there is neither initial position nor initial velocity, then
[tex]x= at^2[/tex]
With our values we have [tex]x = 401.4m, t=4.945s[/tex], rearranging to find a,
[tex]a=\frac{x}{t^2}[/tex]
[tex]a = \frac{ 401.4}{4.945^2}[/tex]
[tex]a = 16.41m/s^2[/tex]
Therefore the final velocity would be
[tex]v_f = v_0 + at[/tex]
[tex]v_f = 0 + (16.41)(4.945)[/tex]
[tex]v_f = 81.14m/s[/tex]
Therefore the final velocity is 81.14m/s
