00:02
Alright, so here from the newton's second lap motion, force acting on a mass is defined as the rate of change of its momentum, right? so this is written by d over dt and rate of change of momentum.
00:20
This mv is momentum, right? now this will be, let this is m dv by d t right? because m is constant right? so we will bring it outside right so this is mv dot right so m is the mass in v the velocity is the velocity is the rate of change of displacement right velocity is d x by d t which is x second dot uh x dot right and if we depreciate it with both sides right so dv by d t is the second derivative of x dot over d t right so this will be this will be v dot and this will be x double dot which is acceleration right this is acceleration this is also acceleration so this is mx double dot so we will take the magnitude on both side right so in part a here, let in part a coming to part a here.
01:45
The post -acting an particle is pectoral in the following palm, right? x -i -t, this is a -p -x -i -g -r -t.
01:58
And we'll substitute, we'll substitute, let par, a -p -x -i -t.
02:07
This is lit this is nx double dot right so if we substitute that this is mx double dot sub i right this will be apop x of i g of t right and m d x this is just the derivative this is apop x of i g of t right and we will write rewrite this equation so if you read out this equation, this will be m dx dot over a pab, x of i, this is g of t, dt, right? so let card this is equation one...