i am in high school and have just the preliminary knowledge of kinetics .I wanted to know in case of non uniform accelerated motion if velocity (in respect of time)is integrated to give displacement.if it turns out to be zero after solving.what is the method to find distance in such a case

actually acceleration is always given as the second derivative of discplacement with respect to time.

 

as a consequence velocity is the integral of acceleration with respect to time, and discplacement is the integral of velocity with respect to time.

 

 

 

hmm I was always a fan of teaching calculus through kinematics, for instance when I learned calculus the derivative was derived by talking about the motion of a train. It makes sense to teach it this way as well considering Newton created the derivative in order to solve certain mechanics problems.

If the velocity changes direction and the value goes negative, and you want to find the toal distance travelled, you would have to use speed (i.e. the absolute value, so it remains nonnegative) in the integral of speed during the time interval.

 

Of course, you'd need to know the speed as a function of time. As CPL Luke implied, take the acceleration if you know that, and integrate twice; the first integral gets you the velocity (still need to use an absolute value in there)