Consider a particle moving along the positive direction of X -axis. The velocity of the particle is given by v = α x ( α is a positive constant). At time t = 0 , if the particle is located at x = 0 , the time dependence of the velocity and the acceleration of the particle are respectively.

Question

Consider a particle moving along the positive direction of X -axis. The velocity of the particle is given by v = α x ( α is a positive constant). At time t = 0 , if the particle is located at x = 0 , the time dependence of the velocity and the acceleration of the particle are respectively., α 2 2 t and α 2 2, α 2 t and α 2, α 2 t and α 2, α 2 4 t and α 2 4

MARKS App · Accepted Answer

Given that, v = α x d x d t = α x ∴ v = d x d t d x x = α d t ∫ d x x = α ∫ d t ⇒ 2 x = α t + c At t = 0 , x = 0 ⇒ c = 0 ∴ 2 x = α t On Squaring, ⇒ 4 x = α 2 t 2 ⇒ x = α 2 t 2 4 On differentiating, d x d t = v = α 2 4 2 t 2 = α 2 t 2 ⇒ a = d v d t = d v d t d x d t = v d v d x = α x d d x α x = α x α x - 1 / 2 2 = α 2 2

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