Can someone please tell me how to do the highlighted part of C? My teacher doesn't know either
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There is no way to get rid of the constant, so I don't know how the answers are getting a single number?
The stationary point is the maximum distance to the right. But i have no idea how to find the maximum distance to the left. It makes sense to me why they said its the boundary (10 seconds) since its velocity has been negative for the longest. I just dont get how they subbed it back into the displacement function when we dont have the constant C?
doesn't matter about C, it's only about how far it is away from the initial position. for example:
we can just take the initial position as 0, so x(0) = 0 = C
so now x(t) = 16t-2t^2 = 2t(8-t)
now sketching this, we see that the maximum distance to the right is 32 cm from the intial position (vertex of the parabola at t = 4), and the maximum to the left is 40cm from the initial position (at t = 10).
it wouldn't really matter if we took x(0) = 10, for example. now
x(t) = 10+16t-2t^2 = 2(5+8t-t^2)
again the maximum here is at the vertex of t = 4s, which has a corresponding x(t) of 42. so how far away is it from the initial position of x = 10? 32cm, same as we got before. so u can just pick any value for the initial position, u just need to make sure that the maximum distances u give are relative to that initial position
