The coordinates of a moving particle at any time t are given by x = α t ⁡ 3 and y ⁡ = β t ⁡ 3 . The speed of the particle at time t is given by

Step-by-step solution

∵ x = α t ⁡ 3 ∴ d ⁡ x d ⁡ t ⁡ = 3 α t ⁡ 2 ⇒ v x = 3 α t ⁡ 2 Again y ⁡ = β t ⁡ 3 ∴ d ⁡ y ⁡ d ⁡ t ⁡ ⇒ v y ⁡ = 3 β t ⁡ 2 Since, v 2 = v x 2 + v y 2 v 2 = ( 3 α t ⁡ 2 ) 2 + ( 3 β t ⁡ 2 ) 2 = ( 3 t ⁡ 2 ) 2 ( α 2 + β 2 ) Or v = 3 t ⁡ 2 α 2 + β 2