I performance test cars with a draggy, it measures the change in position over time... sound familiar? anyway.. see below. I was able to enter my acceleration data in numbers and plot the equation relatively precisely with the below equation.
What I can't seem to figure out is how I can obtain the position of my car (in feet) from the equation; namely, find out at $1320$ ft.. how long it took my car to get there &/or vice versa (enter a time and obtain a distance). I know that I started at $0$ mph & at $130$ mph my car had traveled $2067.32$ feet. I also know at $60$ mph I had traveled $202.73$ feet.
I have tried integrating my velocity equation from $1320$ to $0$... however this rendered no results. Any ideas out there?
$$v=\frac{dx}{dt}$$so$$\int_0^Tv(t)dt=\int_{x(0)}^{x(T)}dx$$ In your case you calculate the integral by summing