The displacement x of a particle varies with time t as x = a e - α t + b e β t , where a , b , α and β are positive constants. The velocity of the particle will

Step-by-step solution

x = a e - α t + b e β t d x d t = - a α e - α t + b β e β t ⇒ v = b β e β t - a α e - α t As t increases, e - α t decreases and e β t increases. So v will increase with time.