How do you find the speed of an object given its mass and kinetic energy (what is the formula)?

   v  =   √ { 2*(KE) ] / m } ; 

Now, plug in the known values for "KE" ["kinetic energy"] and "m" ["mass"] ; 
        
and solve for "v".

Explanation:

The formula is:  KE = (½) * (m) * (v²) ;

  
"Kinetic energy" = (½) * (mass) * (velocity , "squared")

Note:  Velocity is similar to speed, in that velocity means "speed and direction";  however, if you "square" a negative number, you will get a "positive"; since:  a "negative" multiplied by a "negative" equals a "positive".

So, we have the formula:

KE = (½) * (m) * (v²) ;  to solve for "(v)" ; velocity, which is very similar to                                          the "speed"; 

we arrange the formula ;

(KE) = (½) * (m) * (v²) ;  ↔  (½)*(m)* (v²) = (KE) ; 


→ We have:  (½)*(m)* (v²) = (KE)  ; we isolate, "m" (mass) on one side of the equation:

   
→ We divide each side of the equation by: "[(½)* (m)]" ; 

    
           →   [ (½)*(m)*(v²) ] /  [(½)* (m)]  = (KE) / [(½)* (m)] ;

 to get: 

                           →   v²     =   (KE) / [(½)* (m)]
                     
                           →   v²     = 2 KE / m

Take the "square root" of each side of the equation ;

                          →  √ (v²)  =  √ { 2*(KE) ] / m }


                          →     v  =   √ { 2*(KE) ] / m } ; 

Now, plug in the known values for "KE" ["kinetic energy"] and "m" ["mass"]; 
       
and solve for "v".