Recent content by fmiren

Yes, I see this now, what confuses me is how to choose the limits of definite integral in such kind of problems.

Aa, sorry. Ok, I am trying to get it, But then how do I choose the limits of integral? I'm confused. If the problem says that t<t1<t2, I think the natural (which seems natural to me) is t2 and t1. This part confuses me.

If t = t1, and v(t) = v_0, then v_0-c(t-t_1)^2/2 = v_0 which means -c(t-t_1) should be 0? Am I right?

At time t=0 , a car moving along the + x -axis passes through x=0 with a constant velocity of magnitude v0 . At some time later, t1 , it starts to slow down. The acceleration of the car as a function of time is given by: a(t)= 0 0≤t≤t1 -c(t−t1) t1<t2 where c is a positive constants in...

To get the velocity I integrate the accelaeration function and get v_0-c*(t_2-t_1)^2/2 since I think these should be the boundaries of the definite integral. Bu the correct answer is v_0-c*(t-t_1)^2/2 and they integrate from t (upper limit) to t1 (lower limit). Could you please help me to...

Thank you. How does it apply to this problem? Is the function discontinuous at c, e, g, and l points? And what it implies?

It is from a open textbook "College Physics" - https://openstax.org/details/books/college-physics I don't remember any mention of special cases in the text. Could you please explain what they are?

Yes, in one of comments above I included it. a) td b) tc, te, tg, tl c) ta, tb, tf Is it ok now?

At ta it is negative, at tc it is zero.

To be honest, I didn't pay enough attention to it. Now looking at again, I think, yes, ta should be included. But I don't understand why the answer for c) is wrong. Any hint please?

Yes, I think at tc it is also 0. So my answers: a) td b) tc, te, tg, tl c) tb, tf Is it correct now?

Yes, I'm afraid. The only correction that I can make is to a) part: at tl instantaneous velocity should also be 0. Where I'm wrong?

My answers: a) At points d the instantaneous velocity should be greatest since slope of c-d is greatest I think b) At point e and g instantaneous velocity is 0 c) at points b, c, and f instantaneous velocity is negative. Could you please verify my answers?