CDS 2018 PYQ with Answer — The position vector of a particle is r⃗ = 2t²x̂ + 3tŷ + 4ẑ. Then th…

2018 · Q9

The position vector of a particle is r⃗ = 2t²x̂ + 3tŷ + 4ẑ. Then the instantaneous velocity v⃗ and acceleration a⃗ respectively lie

General KnowledgePhysics

Aon xy-plane and along z-direction
Bon yz-plane and along x-direction
Con yz-plane and along y-direction
Don xy-plane and along x-direction

Explanation

Differentiating the position vector r = 2t^2 x-hat + 3t y-hat + 4 z-hat gives velocity v = 4t x-hat + 3 y-hat, which has only x and y components and therefore lies in the xy-plane. Differentiating again gives acceleration a = 4 x-hat, which points purely along the x-direction. No other combination matches: the velocity has no z-component and the acceleration has no y-component. Hence the answer is the xy-plane and the x-direction.