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

Step-by-step solution

Given, x=a e^ - t +b e^ t So, velocity aligned v & = d x d t & =-a e^ - t +b e^ t & =A+B aligned Where, A=-a e^ - t , B=b e^ t The value of term A=-a e^ - t decreases and of term B=b e^ t increases with increase in time. As a result, velocity goes on increasing with time.