s= (Vo)t + (at^2)/2
or
34.8 = 4.28Vo + [a(4.28)^2]/2
In another trial the arm is found to drop 58.3 cm in 5.57 seconds, with the same initial speed and acceleration. Find Vo and a.
you get s = 34.8 and t = 4.28
formula becomes:
34.8 = 4.28(Vo) + (a*4.28^2)/2
you have another trial where s = 58.3 and t = 5.57
formula becomes:
58.3 = 5.57(Vo) + (a*5.57^2)/2
since Vo and a remain the same in both equations, you have 2 equations that need to be solved simultaneously.
those equations are:
34.8 = 4.28(Vo) + (a*4.28^2)/2
58.3 = 5.57(Vo) + (a*5.57^2)/2
simplify these equations to get:
34.8 = 4.28(Vo) + 9.1592(a)
58.3 = 5.57(Vo) + 15.51245(a)
multiply both sides of the first equation by 5.57 and multiply both sides of the second equation by 4.28 to get:
193.836 = 23.8396(Vo) + 51.016744(a)
249.524 = 23.8396(Vo) + 66.393286
subtract the first equation from the second equation to get:
55.688 = 0 + 15.376542(a)
simplify to get:
55.688 = 15.376542(a)
solve for a to get:
a = 3.621620518
go back to either original equation and solve for Vo to get:
Vo = .3805732134
that's your solution.
substitute those values for a and Vo in both your original equations and you will get:
34.8 = 4.28(.38057342134) + 9.1592(3.621620518) = 34.8
58.3 = 5.57(.38057342134) + 15.51245(3.621620518) = 58.3
your solution is confirmed as good.
your solution is:
Vo = .38057342134
a = 3.621620518
you could also have solved both of these equations graphically.
you would do this as shown below:
the 2 equations are:
34.8 = 4.28(Vo) + (a*4.28^2)/2
58.3 = 5.57(Vo) + (a*5.57^2)/2
solve for Vo in both equations to get:
Vo = (34.8 - (a*4.28^2)/2)/4.28
Vo = (58.3 - (a*5.57^2)/2)/5.57
set y = Vo and set x = a and the equations become:
y = (34.8 - (x*4.28^2)/2)/4.28
y = (58.3 - (x*5.57^2)/2)/5.57
graph both these equations as is and then find the intersection of both equations on the graph.
you will get the following graphical solution:
the intersection point is shown.
x = a
y = Vo
x = 3.622
a = .381
these are the same solutions obtained by formula except they are rounded to 3 decimal digits.