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 We know that, velocity, v= d x d t aligned & d d t (a e^ - t +b e^ 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 increases and of term B=b e^ - t increases with time. As a result, velocity goes on increasing with time.