A car is traveling with a velocity v on a circular road of radius r. If it is decreasing it`s speed at the rate of a, then the magnitude of resultant acceleration will be.......

The instantaneous acceleration a_r 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 a_r = 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 a_t = dv/dt = a m/sec² (given)

The tangential acceleration of the car has a constant magnitude of a_t = a m/sec²

The components a_r and a_t are perpendicular to each other and the magnitude of a is given by

resultant accln. a² = a_r² + a_t²

                         resultant accln. (a_res)         =[ a²+(v²/r)² ]^1/2

                                                                       =[ a² +(v⁴/r²) ]^1/2

^Regards

^{Arun(askIITians forum expert)}