While racing on a flat track, a car rounds a curve of 28m radius and instantaneously experiences a centripetal acceleration of 18 m/s2. how fast was the car going? how would you go about doing this?

When a body strictly moves on a curve, it's velocity at a point is tangential to the curve at that point.

Centripetal acceleration is the acceleration that a body experiences by the virtue of change in it's tangential velocity. It is directed towards the centre and mathematically is v^2/R where v is the speed at the instant.

So, 18 = v^2/R
v^2 = 504
v = 6√14