so i have to calculate the maximum velocity and object can reach from a rolling start before having to brake to a given speed (for example to enter a corner)

i have


accelerating

A1 = S_r (distance remaining) =225 .... this is given and can not be changed
A2 = U (initial velocity) =52.8 .... this is given and can not be changed
A3 = V (final velocity) ? ..... this must be found and must equal B2
A4 = a (acceleration) =9.73 .....this is given and cannot be changed

A6 = S_c (distance covered) = =(A3^2-A2^2)/(2*A4) .........requires V to calculate
A7 = t (time taken) = =(A3-A2)/(A4) ...... requires v to calculate

braking

B1 = S_r (distance remaining) = =A1-A6 .......... requires A1 to calculate but must equal B6
B2 = U (initial velocity) = =A3 ......... must be the same as A3
B3 = V (final velocity) = 10 ..........this is given and can not change
B4 = a (acceleration) =-11.98

B6 = S_c (distance covered) =(A3^2-A2^2)/(2*A4) ........ must equal B1 requires B2 to calculate
B7 = t (time taken) = =(A3-A2)/(A4) ........ requires B2 to calculate


my current method is just change A3 manually until i get B2 and B6 as close to equal as i can using 2 decimal places but this is time consuming in accurate and ruins the efficiency of my worksheet

if somebody could please aid me in resolving this i would extremely grateful, i have iterative calculation turned on but am not sure what functions i need to enter to get this to work, or is someone out there know an equation to calculate this you would truly make my day

a great big thanks in advance for your time and efforts