Xi=0m
Xf= 105m
a= 7.66m/s^2
Vi= 0m/s ( I am assuming that the initial velocity was zero. I hope the question said something like "started from rest" or something)
Vf= UNKNOWN
First, I would use this equation to find time:
[tex]
( x_{f} - x_{i} ) = v_{i} (t) + \frac{1}{2}at^{2} [/tex]
[tex]105= (0)t + 0.5(7.66)( t^{2}) [/tex]
[tex]105=3.83( t^{2} )[/tex]
[tex] \frac{105}{3.83} = t^2[/tex]
[tex] \sqrt{ \frac{105}{3.83}} =t[/tex]
[tex]t= 5.24 s[/tex]
Once you have found time, use this equation to find final velocity:
[tex] v_{f} = v_{i} +at[/tex]
[tex] v_{f} = 0 + (7.66)(5.24)[/tex]
[tex] v_{f} = 40.11 m/s[/tex]
Does this help?
