Question

A particle located at x = 0 at time t = 0:,starts moving along x-direction with a velocity v = α√x . The displacement of the particle varies with time as [AIEEE 2006]
(a)t² , (b) t. (c) t½ (d) t³​

Answer 1

Explanation:

• Given, v = α√x
• dx/dt =α√x
• dx/√x =αdt

On integrating , we get

• ₀∫ˣdx/√x = ₀∫ᵗαdt
• ∵[at t= 0 x = 0 and let at any time t ,particle be at x]
• [x½/1/2]₀ˣ= αt
• or ,x½ = αt/2
• or x= α²/4×t² or x ∝ t²

Hence option (a) is correct .