00:01
So here the solution for this problem is we'll get the equation as dv divided by d t.
00:07
Dv divided by d t is equals to 9 .8 multiplied with 5 minus v divided by 5.
00:17
So we'll get the equation as bv divided by 49 minus v is equals to d t divided by 5.
00:26
Where 49 minus v is equal to 0 and minus dv is equals to da so we'll get the equation as minus the a divided by a is equal to d t divided by 5 so by integrating the equation on both sides we'll get the equation as minus l n of a is equal to p divided by 5 plus so by simplifying this further we'll get the equation as ln of a is equals to minus t divided by five plus k.
01:10
So here we will get the equation as ln of 49 minus v is equals to minus t divided by minus t divided by five plus k.
01:25
But here v of 0 is equal to 0 is given so the equation will be ln of 49 minus 0 is equal to 0 plus k which means ln of 49 minus 0 is equal to k so this will come as 3 .9 is equal to k which means ln of 49 minus v is equals to minus t divided by 5 plus 3 .9.
02:04
So as for the first condition, as for the first condition, the 98 % of limiting velocity will be 49 minus v is equals to e power negative to e power negative to e.
02:29
Divided by 5 multiplied with e power 3 .9.
02:35
So this will give us the equation as 49 multiplied with e power minus t divided by 5 multiplied with 49 minus v is equal to v.
02:52
So here the limit t approaching infinity of v is equals to 49 minus 49 .4 divided by e power t divided by 5...