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Question

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

A
Decrease with time
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B
Be independent of α and β
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C
Drop to zero when α=β
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D
Increase with time
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Solution

## The correct option is B Increase with timeGiven, x=ae−αt+beβtWe know that, velocity, v=dxdt ddt(ae−αt+beβt) =−aαe−αt+bβeβt =A+Bwhere, A=−aαe−αt,B=bβeβtThe value of term A=−aαe−αt increases and of term B=bβe−βt increases with time. As a result, velocity goes on increasing with time.

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