in this video I will talk about the work done by a varying force the force is not constant so the force is not constant how do you calculate the work done to in general we have a study the work done is equal to the force time displacement and times the cosine theta and theta is the angle between the force and the displacement and this formula this equation is valid only when the force this force is a constant force but now as the displacement changes as the displacement changes the force also changes then how do you calculate thee what work done we'll be talking into this problem so here we have given a constant force and the mass of the object is 2 kilogram and we are applying this force onto this to look at an object and this force is now applied from x equals to 0 meter to 5 meter or we have to move this 2 kilogram object a distance of 5 meter and at x equals to 0 or at initially the object is at rest and now what do we have to find out what is the amount of work done and what is the velocity of the object when it has moon x equals to 5 meter okay so let's do that so now when the work is change or sorry when the force is changing the amount of work done can be given by this formula or by integrating the force and the displacement so this is the instantaneous force and that be the tiny displacement and then now if you integrate then that if you the total amount of work done and again he and I'm not using any cosine component or not using the vector here and simply because the force and the displacement are in the same direction or we are talking about the motion in one dimensional so the force is a varying force which is given five x squared plus 9x minus 5 and DX we now need to integrate this one so you need to keep in mind that this is the integration for X to the M into DX which is X to the M plus 1 divided by n plus 1 so now let's use this formula to in to integrate each term so you see now the power has increased by + 1 so it will be 5x cubed divided by 3 again x squared divided by 2 and then minus 5 into X so just by using this formula we will get we integrated this expression now and now we have to put a limit 5 to 0 so first we go plug in 5 5 3 and then we're going to plug in 5 here 5 Q then 5 squared and our 5 times X and now we're going to plug in the limit here so each term has X so each term will be jail that's the reason aperture here when you do the calculation what you get is the the total amount of work done is about 296 Joule thus the total amount of work done the second part is asking what is the velocity at the end if you keep pushing an object then it will have a certain velocity at the end and what is that velocity is so in order to calculate that velocity we're going to use or the work-energy theorem this is the work-energy theorem the first term is the final kinetic energy remember this is the final kinetic energy ke a stands for the kinetic energy and this is the initial kinetic energy again ke s transport the ki netic embassy there's a formula for the kinetic energy so the change in kinetic energy is equal to the amount of work done and the object is a starting from rest so if the object is starting from rest its initial velocity will be zero so that's the initial speed we can probably call it so this is zero and with the work done we already have calculated the work done which is to ninety five point eight now let's plug in the other values have that mass is given which is 2 kilogram as I said here the mass is 2 kilogram mass the mass is given we're now finding the final velocity VF s squared and again this is zero because the initial velocity 0 or the object it is starting from rest if we solve it that we get the the final velocity which is 17 point 2 meter per second so the thing you need to remember in this problem is we have used two very important concept in the work done how to calculate the work done when the force is changing or the varying force and the second thing we used is the word energy theorem okay if it know the difference in the kinetic energy we can calculate the work done or you can or if you know the work done we can calculate the velocity so this is it for this for this video again if you have any questions write down your quotient in the comment section below or if you have any suggestion any feedback please wipe down your suggestion in the conversation below and at the end do not forget to Like share and subscribe the channel thank you