So, let us say a body moves with 10 m/s, mass = 10 kg. At time t=0 a force of 30 N is acting on it. Gradually (linearly) the force increases and finally it becomes 130 N after a period of 2 second .
Now, we can say that change in force every second = $30+50t.$
Now, $dp = dt (30+50t)$
Now, integrating and putting limits as t = 0 to t= 2 seconds. We get final momentum = $160\ kg/m s^2$. Now, we cannot say that F=160/2 since value of instantaneous force is not constant.
Part 1: Finding final velocity and momentum:
If I say $130N=10*a $, then a=$13\ m/s^2.$
Final velocity = u+at = 10 + (13)(2) = 36m/s.
Now, Final momentum becomes $m*v =10*36$ = $360\ kgm/s^2. $
Q1 Now, why is 160 not equal to 360 as the final momentum?
Q2 are final velocity and acceleration correct?