Rearrange equation of motion for time

Question

One of the "SUVAT" equations of motions is: $$s=ut+\frac{1}{2}at^2$$ Which relates distance, $s$, in meters, to initial velocity, $u$, in $\dfrac{m}{s}$, time elapsed, $t$, in seconds and acceleration, $a$, in $\dfrac{m}{s^2}$.

I have distance, acceleration and initial velocity, I'd like to calculate $t$. I suspect this requires the use of calculus but I'm not versed with what question to ask search engines to find the right mathematical approach to solve for $t$.

Answer 1

If we write the equation in the form $$\frac{1}{2}at^2+ut-s=0$$ and assuming $a\ne 0$ using the quadratic formula $$x=\frac{-B\pm\sqrt{B^2-4AC}}{2A}$$ where A, B and C relate to $$Ax^2+Bx+C=0$$ we get $$A=\frac{1}{2}a$$ $$B=u$$ $$C=-s$$ $$t_{1,2}=\frac{-u\pm\sqrt{u^2+2as}}{a}$$