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Question

The displacement x of a particle varies with time t as x=aeαt+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 time
Given,
x=aeαt+beβt
We know that, velocity, v=dxdt
ddt(aeαt+beβt)
=aαeαt+bβeβt
=A+B
where, A=aαeαt,B=bβeβt
The value of term A=aαeαt increases and of term B=bβeβt increases with time. As a result, velocity goes on increasing with time.

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