To answer the original question, the 'whip' or 'slingshot' effect that many people (especially track announcers) talk about is not fully based in science. There is certainly some tangential acceleration for a couple steps but it is more of a perception than anything else.
They say one of the secerts to running a good 200m, is too have the
whipping effect at the end of the corner to the straight away,
which will carry even more speed to the line.
You learn about curve motion and centripetal forces/acceleration in school physics. The perception you feel on the curve is known as the centrifugal force-which actually dosen't exist, it's just a feeling that opposes the centripetal force that is theoretically pulling you toward the centre of the circular motion that you are running in. Your velocity at any one point is at a tangent to the circular motion you are moving in, yet because of the centripetal force towards the centre of the circle, a centripetal acceleration is 'induced' in the same direction as the force-towards the centre of the circle-which causes your motion to become circular.
A more in depth study of the actual 200m race science would provide you with exact details as Mike mentioned something about tangential acceleration, but the basics are about the centripetal force and acceleration that acts on any object undergoing circular motion, and the weird sideways sensation you feel is only a reaction in opposition to the centripetal force acting on you, a little bit similar to the jolt you get in a lift when you feel your insides seem to stay in the same place whilst your body moves down with the lift – i've heard rollercoasters provide similar sensations but i've never gone on one (I have a phobia of heights).