A particle located at 𝑥 = 0 at time 𝑡 = 0, starts moving along the positive 𝑥-direction with a velocity ‘𝑣’ that varies as 𝑣 = 𝑎√𝑥. The displacement of the particle varies with time as

Question : A particle located at 𝑥 = 0 at time 𝑡 = 0, starts moving along the positive 𝑥-direction with a velocity ‘𝑣’ that varies as 𝑣 = 𝑎√𝑥. The displacement of the particle varies with time as

(A) 𝑡

(B) t^{\dfrac{1}{2}}

(C) t^{3}

(D) t^{2}

Answer : option (D)

Solution :

A particle located at 𝑥 = 0 at time 𝑡 = 0, starts moving along the positive 𝑥-direction with a velocity ‘𝑣’ that varies as 𝑣 = 𝑎√𝑥. The displacement of the particle varies with time as
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