Ansswer Part G only.*I do not accept any handwriting work?* The position of a mo
ID: 2864217 • Letter: A
Question
Ansswer Part G only.*I do not accept any handwriting work?*
The position of a moving object is given by the function s(t), where s is measured in feet and t in seconds. We determine that the velocity is v(t) = 4t + 1 feet per second. How much does the position change over the time interval [0,4]? Does this give you enough information to determine s(4), the position at time t = 4? If so, what is s(4)? If not, what additional information would you need to know to determine s(4)? Suppose you are told that the object's initial position s(0) = 7. Determine s(2), the object's position 2 seconds later. If you are told instead that the object's initial position is s(0) = 3, what is s(2)? If we only know the velocity v(t) = 4t + 1, is it possible that the object's position at all times is s(t) = 2t^2 + t - 4? Explain how you know. Are there other possibilities for s(t)? If so, what are they? If, in addition to knowing the velocity function is v(t) = 4t + 1, we know the initial position s(0), how many possibilities are there for s(t)?Explanation / Answer
v (t)=4t+1
by integrating we get s (t)
s (t)=2t^2+t+c , where c is an arbitrary constant
We know the initial value of s (0) so from this we can calculate c. means c is fix so there is only one possibility for
s(t).