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`        THe motion of a body is given by the equation dv(t)/dt=6.0-3v(t), where v(t) is speed in m/s and t in sec. if a body was at rest at t=0 	the terminal speed is 4m/s.	the speed varies with time as v(T)=2(1-e^(-5t)) m/s.	the speed is 0.1 m/s when the acceleration is half the initial value.	the magnitude of the initial acceleration is 6.0 m/s^2`
5 years ago

Nicho priyatham
625 Points
```							by integration we get v=2-e-3tso first 3 options or wrong and  ans is 4 as intial a is 6 plz approve if useful and incase of any doubts ask in ans box
```
5 years ago
Archita
132 Points
```							can u explain how did u get v=2-e^-3t
```
5 years ago
Nicho priyatham
625 Points
```							given dv(t)/dt=6.0-3v(t)  so dv(t)/6.0-3v(t)=dt now take integral on both sidesso on ∫ we get v=2-e^-3t   PLZ APPROVE IF USEFULL
```
5 years ago
Nicho priyatham
625 Points
```							R U having problem in integration …...? or can u integrate the given functionif u dont no integration plz let me know i will help u out
```
5 years ago
Archita
132 Points
```							i just know the basics of integrationi dont know how to integrate the above function
```
5 years ago
Nicho priyatham
625 Points
```							k i will help u on it  after 7;30 today
```
5 years ago
Archita
132 Points
```							im really sorry but i have to do my class work for tmrw.thanks for helping mejust write the explanation here after 7:30.if i have any doubt in that i’ll post it here tmrw.thank you so much
```
5 years ago
Nicho priyatham
625 Points
```							integration in lower levels is formula based so learning formulas is mustsince u no basics u might know all formulas if u dont know them learn themnow u need to remember that if ∫f(x)dx=g(x)+c then ∫f(ax+b)dx=(1/a)g(ax+b)+c _____________(1)so now we no that ∫df(x)/f(x)=Inf(x)+c here we have  dv/dt=6.0-3vso  ∫dv/6.0-3v=∫dt  so from 1 we get(-1/3)(log(6-3v)-log(6)=t  (u need to  take limits from o to v on LHS  and 0 to t on RHS)now log (1-(v/2))=-3t so e-3t =1-(v/2)so v=2(1-e-3t ) PLZ APPROVE if usefull in  case of any doubs ask  in ans box
```
5 years ago
Archita
132 Points
```							thank u so much for taking the trouble.i totally understood it.
```
5 years ago
Nicho priyatham
625 Points
```							ur welcomeits my plessure
```
5 years ago
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Course Features

• 110 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions