Question

The displacement x of a particle varies with timex=ae−αt+beβt, where a,b,αandβ are positive constants. The velocity of the particle will -

Answer 1

Answer:

Given,

x=ae

−αt

+be

βt

We know that, velocity, v=

dt

dx

dt

d

(ae

−αt

+be

βt

)

=−aαe

−αt

+bβe

βt

=A+B

where, A=−aαe

−αt

,B=bβe

βt

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.