How Do You Rearrange the Equation x = x₀ + V₀t + ½at² to Solve for V₀?

[petern]

How can I arrange x = x_o + V_o t + (1/2)(a)(t)^2 so that I can solve for V_o algebraically?

 

[Astronuc]

To solve for V_o, one would need to x(t) and t, then it would be just a matter of rearranging the terms, or one writes

(x(t) - x_o - 1/2 at²)/t = V_o, or

(x(t) - x_o)/t - 1/2 at = V_o


So I'm puzzled about the question.

Finding V_o depends on what other variables are known, and applying the appropriate equation of motion. Does one assume that acceleration is constant?

 

[petern]

This is the original problem: What's the velocity of a ball thrown vertically from a cliff of 95 meters height that strikes the ground in 5 seconds?

You would use the equation I previously listed but I don't know how to solve for it algebraically.

t = 5 s
a = 9.8 m/s^s
x_o = 0 m
x = 95 m
V_o = ?

 

[Astronuc]

Well consider how far something can fall under freefall in 5 seconds.

If that distance is greater than 95 m, then the ball must be thrown upward to some point, then it falls downward. Then the ball must travel to some height h, in time t_up, then fall from height 95 m + h during time 5 s - t_up.

See is this reference is helpful.
http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html