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Question

The displacement of a particle varies with time t, x=aeαt+beβt, where a, b, α and β are positive constants. The velocity of the particle will
  1. Go on decreasing with time
  2. Drop to zero when α = β
  3. Go on increasing with time
  4. Be independent of  α and β


Solution

The correct option is C Go on increasing with time

x=aeαt+beβt

Velocity  v=dxdt=ddt(aeαt+beβt)

=aeαt(α)+beβt(β)=aαeαt+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

 

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