The displacement 𝑥 of a particle varies with time 𝑡, 𝑥 = 𝑎𝑒 −𝛼𝑡 + 𝑏𝑒 𝛽𝑡, where 𝑎, 𝑏, 𝛼 and 𝛽 are positive constants. The velocity of the particle will

April 14, 2022

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Physics Problems

Question : The displacement 𝑥 of a particle varies with time 𝑡, 𝑥 = 𝑎𝑒 −𝛼𝑡 + 𝑏𝑒 𝛽𝑡, where 𝑎, 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

(D) Go on increasing with time

Answer : (D)

Solution :

The displacement 𝑥 of a particle varies with time 𝑡, 𝑥 = 𝑎𝑒 −𝛼𝑡 + 𝑏𝑒 𝛽𝑡, where 𝑎, 𝑏, 𝛼 and 𝛽 are positive constants. The velocity of the particle will