# A CAR IS TRAVELING WITH A LINEAR VELOCITY v ON A CIRCULAR ROAD OF RADIUS R IF IT IS INCREASING ITS SPEED AT THE RATE OF 'a' MS^-2 THEN THE RESULTANT ACCELERATION WILL BE

Ramesh V
70 Points
14 years ago

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

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Naga Ramesh
IIT Kgp - 2005 batch