How to find Time when you know the Distance and Acceleration

Question

The Distance is 0.1693 meters and the Acceleration is 10 m/s^2. What equation would I use to find time this certain question.

Answer 1

We assume the object starts at rest, so at $t=0$ we have $d(0)=0, v(0)=0, a(0)=10$.

so the initial displacement, and velocity is zero.

then we solve for $v(t)=\int_0^ta(x)dx=10t$ This is a function which gives us the velocity at a time $t$ in seconds. Then we can solve for $d(t)=\int_0^tv(x)dx=\int_0^t10xdx=\frac{10t^2}{2}$ which gives us the distance after $t$ seconds. Then we set $d(t)=0.1693$ and solve for $t$.

the reason we took both integrals from 0 is because of the initial conditions were assumed to be 0. If we had some other initial position or initial velocity, we would take the integrals from there.