The displacement x of a particle varies with time t as x = ae-1 + be

1.	The displacement x of a particle varies with time t as x = ae-1 + belt, where a, b, a, and ß are positiveconstants. The velocity of the particle will[AIPMT (Prelims)-2005]
Answer» ong>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.

The displacement x of a particle varies with time t as x = ae-1 + belt, where a, b, a, and ß are positiveconstants. The velocity of the particle will[AIPMT (Prelims)-2005]

Answer»

ong>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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The displacement x of a particle varies with time t as x = ae-1 + belt, where a, b, a, and ß are positiveconstants. The velocity of the particle will[AIPMT (Prelims)-2005]​

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The displacement x of a particle varies with time t as x = ae-1 + belt, where a, b, a, and ß are positiveconstants. The velocity of the particle will[AIPMT (Prelims)-2005]