Question

# The displacement of a particle varies with time t, x=ae−αt+beβt, where a, b, α and β are positive constants. The velocity of the particle willGo on decreasing with timeDrop to zero when α = βGo on increasing with timeBe independent of  α and β

Solution

## The correct option is C Go on increasing with timex=ae−αt+beβt Velocity  v=dxdt=ddt(ae−αt+beβt) =ae−αt(−α)+beβt(β)=−aαe−αt+bβeβt From the above equatin itself we can tell that velocity will increase with time since the negative component will decrease with increase in  time and positive component will increase

Suggest corrections