Q17b
acceleration a = -2cos t is positive if -2cos t > 0
i.e. if cos t < 0
Now cos t is < 0 for pi/2 < t < 3pi/2 (if you are familiar with the graph of y = cos t)and again and again later every 2 pi secs later.
For Q14, if you can do parts a, b and c, you are already doing very well.
For Q14d: 1st 4 secs, particle moves 32m to the right. 4 secs later it reverses direction (moving left) and returns to its original position, travelling another 32m. 2 secs later, it moves another 40m to the left. Therefore in the 10 secs, particle has travelled 32m + 32m + 40m = 104m. .: avg speed = 104m/10 sec = 10.4m/sec. (its position at t = 10 sec is x = -40m, i.e. its displacement is -40m)
I think many of these questions are rather difficult for students of 2U Maths. Problem is not that the area is all that difficult. Problem I think is, even before you do the questions, most people do not have a good idea of basic and simple concepts of distance, displacement, velocity and speed. You also need to know basic differentiation and integration.
I don't know how you have been taught. I would just love to stand before a class to make all these ideas clear, before you embark on working on the exercises on motion.
