please help...maths

[SoniaKapoor]

please help me with this question

[Amit Goyal]

Let v(t) denote the velocity at time t.
You are given dv(t)/dt = 8 - 6t
also v(1) = 25
Solving the above differential equation, we get
v(t) =  8t - 3(t^2) + 20
Integrating v(t), we get
s(t) = [4t^2 - t^3 + 20t + s(0)]
Therefore, s(4) - s(2) =  [64 - 64 + 80 + s(0)] - [16 - 8 + 40 + s(0)] = 32

[SINGHAM]

Sir, I got this. But, How did you get s(0) as integral constant in s(t) = [4t^2 - t^3 + 20t + s(0)]  ?

Also, will such physics questions be asked in ISI or DSE entrances? I could solve it myself if I knew that d(v(t))/dt=acc. and d(s(t))/dt=v(t) but am now afraid that i will also have to learn terminologies other than econ and math

[SoniaKapoor]

Thanku sir :)

[Amit Goyal]

That's obvious. Anyways, you can verify it by putting t = 0 on both sides of
s(t) = [4t^2 - t^3 + 20t + s(0)]

I have never seen a problem related to topics such as this (velocity, acceleration and distance) in any of the past years of DSE or ISI. So chances are very low that they ask something like this. I suggest just relax and prepare according to what they have asked in the past.

[SINGHAM]

Thank you, so much Sir!

I tried to follow AIEEE books for maths, but I could not understand them. Then I read your post saying 11th & 12th std. books of NCERT are good for ISI entrace. Are they sufficient? I am really nervous as there is only one month left! If I solve all the past year papers, will it be enough for math section?

[The Villain]

NCERT is no good for ISI...do past yrs plus if u have the book which ISi prescribes for testing maths

[SINGHAM]

OK