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The instantaneous acceleration ar pointing towards the center of the circle is called radial acceleration or centripetal acceleration. The radial component causes a change in direction and its magnitude is given by ar = v2/r, where r is the radius of curvature at the point in question.
The tangential component causes a change in speed and its magnitude is given by at = dv/dt = a m/sec2 (given)
The tangential acceleration of the car has a constant magnitude of at = a m/sec2
The components ar and at are perpendicular to each other and the magnitude of a is given by
resultant accln. a2 = ar2 + at2
resultant accln. (ares) =[ a2+(v2/r)2 ]1/2 =[ a2 +(v4/r2) ]1/2
Regards
Arun(askIITians forum expert)
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