The displacement π‘₯ of a particle varies with time 𝑑, π‘₯ = π‘Žπ‘’ βˆ’π›Όπ‘‘ + 𝑏𝑒 𝛽𝑑, where π‘Ž, 𝑏, 𝛼 and 𝛽 are positive constants. The velocity of the particle will

Question : The displacement π‘₯ of a particle varies with time 𝑑, π‘₯ = π‘Žπ‘’ βˆ’π›Όπ‘‘ + 𝑏𝑒 𝛽𝑑, where π‘Ž, 𝑏, 𝛼 and 𝛽 are positive constants. The velocity of the particle will

(A) Go on decreasing with time

(B) Be independent of 𝛼 and 𝛽

(C) Drop to zero when 𝛼 = 𝛽

(D) Go on increasing with time

Answer : (D)

Solution :

The displacement π‘₯ of a particle varies with time 𝑑, π‘₯ = π‘Žπ‘’ βˆ’π›Όπ‘‘ + 𝑏𝑒 𝛽𝑑, where π‘Ž, 𝑏, 𝛼 and 𝛽 are positive constants. The velocity of the particle will

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