If a ball is dropped, how long must it fall to attain a velocity of 12.55m/s?

I shall show you the calculus solution

$$\\\ddot{y}=9.8\\\\ \dot{y}=9.8t+c\\\\ when \;\;t=0\;\;\dot{y}=0\;\;so\;\;c=0\\\\ \dot{y}=9.8t\\\\ $Find t when $\;\dot{y}=12.55\\\\ 12.55=9.8t\\\\ t=\frac{12.55}{9.8}=1.28sec$$

There you go - that was pretty simple too.  :)

did you need to use physics formula or calculus?

If a ball is dropped, how long must it fall to attain a velocity of 12.55m/s?

I will assume that you are on Earth near seal level      gravity=9.8m/s^2

a=9.8,   u=0,   v=12.55,   t=?

v=u+at

12.55=0+9.8*t

12.55=9.8t

$${\frac{{\mathtt{12.55}}}{{\mathtt{9.8}}}} = {\frac{{\mathtt{251}}}{{\mathtt{196}}}} = {\mathtt{1.280\: \!612\: \!244\: \!897\: \!959\: \!2}}$$

1.28 seconds

If you need to use calc you can ask and it shall be done.

That linear formula looks pretty straight forward to me, Melody......

Is it more confusing with calculus???

Yep...equally easy......