A particle moves along the curve `(x^(2))/(9) +(y^(2))/(4) =1`, with constant speed `v`. Express its "velocity vectorially" as a function of `x,y`.

A particle moves along the positive branch of the curve y = (x^(2))/(2) where x = (t^(2))/(2),x and y are measured in metres and t in second. At t = 2s , the velocity of the particle is

A particle moves along the positive branch of the curve y = (x^(2))/(2) where x = (t^(2))/(2),x and y are measured in metres and t in second. At t = 2s , the velocity of the particle is

A particle moves along the curve x^(2)=2y . At what point, ordinate increases at the same rate as abscissa increases ?

A particle moves along the curve x^(2)=2y . At what point, ordinate increases at the same rate as abscissa increases ?

A particle moves along the curve y=(4)/(3)x^(3)+5 . Find the points on the curve at which the y - coordinate changes as fast as the x - coordinate.

A particle moves in the x-y plane according to the law x=t^(2) , y = 2t. Find: (a) velocity and acceleration of the particle as a function of time, (b) the speed and rate of change of speed of the particle as a function of time, (c) the distance travelled by the particle as a function of time. (d) the radius of curvature of the particle as a function of time.

A particle moves along a path y = ax^2 (where a is constant) in such a way that x-component of its velocity (u_x) remains constant. The acceleration of the particle is