A particle moves in the x y -plane with velocity v =x i +y t j . At t= x 3 y , the

Step-by-step solution

Given, velocity of particle is v =x i +y t j So, | v |=v= x^2+y^2 t^2 Magnitude of tangential acceleration is a_t= d v d t = 0+2 t y^2 2 x^2+y^2 t^2 or a_t= t y^2 x^2+y^2 t^2 Now, substituting t= x 3 y , we get a_t= x 3 y y^2 x^2+y^2 ( x^2 3 y^2 ) a_t= 3 y 2 Also, total acceleration of particle is a = d v d t array ll & a = d d t (x i +y t j ) & a =y j array or magnitude of total acceleration is a=| a |=y Hence, normal acceleration is a _n= a _ total - a _ tangential So, a_n= | a _n |= magnitude of normal accelerat