A car enters a turn of radius of curvature r =15.m at a speed of 15 m/s. At this

Question

A car enters a turn of radius of curvature r =15.m at a speed of 15 m/s. At this instant of time, the magnitude of its acceleration is observed to be 20. m/s2. What can one conclude about the rate of change of the speed of the car?
(A) The speed of the car is not changing with time. (B) The speed of the car is increasing with time. (C) The speed of the car is decreasing with time. (D) The speed of the car is changing with time,but from the vector magnitudes v,r,and a alone, one can not conclude if the speed of the car is increasing or decreasing with respect to time?

Explanation / Answer

when the object moves around a circle , it has a tangential acceleration and also has a centripetal acceleration.

the tangential speed v is the magnitude of tangential velocity vector.Even when the magnitude of the tangential velocity is constant, an accelerationis present,since the direction of the velocity changes continuously.

here circular acceleration is given by the relation a(circular) = v^2/r

                                                                                         = (15)^2/15

                                                                                         = 15 rad/sec^2

so the body is in accelerating.hencce the speed of the car increasing.

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