I'm having a really hard time figuring this one out. At first glance it seems very trivial, but I think it is not. This is not a homework assignment but rather a calculation I need to do for personal reasons. The problem is as follows: An object is accelerated along a distance of s. We have a linear relationship between acceleration and the distance travelled. We also know the acceleration at the beginning and at the end of s to be a0 and a1. Hence the acceleration at the distance s1 is (for s1<s or s1=s) a = a0 + (a1-a0)/s * s1 Now I would like to know the velocity of the object at s1 and the time it takes to get there. Note that the acceleration only changes linearly with the distance but not with the time. And how can you derive the functions a(t), v(t) and s(t) with the information given? What am I missing? If you need more information on the problem, feel free to ask. Any help would be much appreciated. Thanks.