A particle starts from rest and performing circular motion of constant radius with speed given by v = α x where α is a constant and x is the distance covered. The correct graph of magnitude of its tangential acceleration a t and centripetal acceleration a c versus t will be

Step-by-step solution

In circular motion, tangential acceleration is obtained due to change in speed while radial acceleration is obtained due to change in direction, i.e., a t   = d v d t   =   d v d x . d x d t   = v d v d x and, a r   =   ω 2 r   =   v 2 r as, v = α x ⇒ d x d t = α x ⇒ x = α 2 t 2 4 a t = v d v d x = α x · α 2 x = α 2 2 = constant. So, the graph will be a straight line, parallel to time axis. Now, a c = v 2 r = α 2 x r =