What you're looking for is no easy task.
For example you ask:
For example, when it hits the curve, it has to slow down. When it hits
the hard 90 degree angle, it has to almost come to a stop, but then
accelerates out.
For argument's sake assume the car enters a curve that is part of a perfect circle, then in order to stay on the curve a centripetal force $\mathbf{F_c}$ must act on the car:
$$|\mathbf{F_c}|=\frac{m|\mathbf{v}|^2}{\mathbf{r}}$$
where $m$ is the mass of the car, $\mathbf{v}$ is the tangential velocity vector and $\mathbf{r}$ the radius vector.
For an unbanked turn, $\mathbf{F_c}$ must be provided by friction with the road surface:
$$|\mathbf{F_c}|=m|\mathbf{g}|\mu$$
with $\mu$ the friction coefficient.
So that:
$$|\mathbf{g}|\mu=\frac{|\mathbf{v}|^2}{\mathbf{r}}$$
from which the maximum speed $|\mathbf{v}|$ for that turn can be calculated.
But for real tracks, like the one you depict, the turns don't have a constant radius. Instead the concept of curvature could be used.
Probably the safest way to navigate a given turn is to calculate a maximum $\mathbf{v}$ for the point of minimum curvature in the whole bend, then take the whole turn at that velocity.
For example for the left, $180^{\circ}$ turn, curvature is clearly smallest at the 'top'. Note also that "$180^{\circ}$" does not help us calculate the forces acting on the car, in physics that number has no real use.
For $90^{\circ}$ turns the curvature becomes momentarily $0$ and the car must momentarily stop ($\mathbf{v}=0$)
To calculate the accelerations/decelerations in between turns, you have to think like a racing driver: accelerating from one bend, then decelerating again to prepare for the next bend.
I'm trying to do a really basic simulation of a body (eg car) moving
along the line and keep it feeling natural with acceleration and
deceleration.
I don't think there's a simple algorithm that would allow to do this. Everything depends on maximum velocity of the car, its power and its maximum braking force.
