The displacement x of a particle varies with time t
as x = ae-1 + belt, where a, b, a, and ß are positive
constants. The velocity of the particle will
[AIPMT (Prelims)-2005]
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Explanation:
Given,
x=ae−αt+beβt
We know that, velocity, v=dtdx
dtd(ae−αt+beβt)
=−aαe−αt+bβeβt
=A+B
where, A=−aαe−αt,B=bβeβt
The 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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