Alevel maths help on mechanics question

https://imgur.com/gallery/iPmI7AS
How do I do this question?

For part a I differentiated v to get acceleration, set this equal to 0 and get t as 0.75 seconds

For part b I set v equal to 0 and get t is 3.5 seconds and then integrated v and subbed in t is 3.5 into this to get -38.79 m is this correct? If not could someone please give some pointers

Integrating v from t=0 to 3.5 should be ok. However velocity is +ive in this region, so your distance/displacement should be +ive? Upload what youve done?

https://imgur.com/gallery/DAYHqVx
This is my working out. Could u check part a and b please?

Seems roughly ok, but do you know why you get a negative displacement for b)?
Also, it would be better to write the definite integral to make the limits clear. If you do an indefinite, you need to include the integration constant.

Oh okay thanks. I rewrote it using indefinite integral and get 55.46. I see what I did wrong cuz I just ignored the t is -2 solution. Thanks for your help

Err, I think youve made things worse, so my help wasnt that good ..

Wait where did I go wrong?
https://imgur.com/gallery/lYZpauP

For a definite integral you need ot put the limits on the integral sign, not just bring them in at the end.
The lower limit should be the obvious one when the "simulation" starts.

The question tells you it wants the distance between O and P. O is ...

Could u do the question and tel me what u get for the distance of P from O at the instant when P changes its direction of motion. In the question it says point O is on the line but it doesn’t specific whether that O is the origin

Yes it does, at the start. O is the position at time t=0.

Oh my god I’m an actual idiot okay so O is in the origin so do I divide by answer of 55.46 by 2? Or am I doing it completely wrong?

You integrate velocity from O to P, which is pretty much what you were doing originally.

And for the upper and lower number on the integral I use 3.5 and 0? To get s is 38.79?

Yes.