Acceleration using time and distances A car crosses 10m distance from point A to point B in 1 second, next 10m distance from point B to point C it crosses in 0.8s.  Having distances and times is it possible to calculate acceleration and speed at points A,B,C?

No, it is not possible since there are multiple ways in which a car could achieve these times using different speeds.
It could, for example stay at point A for 0.5 seconds not moving at all. Then travel at a speed of 20m/s for exactly 0.5 seconds passing point B at 1 second. From point B on it could travel at 12.5 m/s reaching point C after 1.8s as wished.
The same can however be achieved by just not waiting at the beginning.The car could travel at 10m/s from point A to B and then at 12.5 from B to C.
This does also satisfy the times that you stated but the car crosses the B point only half as fast.
That said as your question is tagged as quadradics it is possible to determine the speeds assuming constant acceleration.
Under constant acceleration a the positions s after time t is given by:
s(t) = 0.5a*t^2 + v_0*t+s_0
We already now that s(0) = 0 and that s(1) = 10m and s(1.8) = 20m.
plugging these into the formula we get two equations.
I.:  s(1) = 10m = 0.5a*(1s)^2 + v_0*1s 
II.: s(1.8) = 20m = 0.5*a*(1.8s)^2 + v_0 * 1.8s
These are two equations with two unknowns, namely v_0 and a. Solving this system of equations will yield the correct answers.
