Question

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]​

Answer 1

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.