Editing Talk:Speed (section)

== If s is the length of the path (also known as the distance) travelled until time t, the speed equals the time derivative of s ==

I think this is not accurate. If in one dimension point A is 1 meter away from point B at time 0 and its speed is 6 m/s for all time, the antiderivative of speed is 6t + c. The c is 1, but for the expression to be the distance travelled c would have to be equal 0. Body A did not travel that first meter, it was already one meter away. In fact, the constant of integration would always have to be 0, which is not the case. [[Special:Contributions/2.36.100.158|2.36.100.158]] ([[User talk:2.36.100.158|talk]]) 20:46, 5 April 2024 (UTC)
:No, you are wrong. "f is the derivative of g" does ''not'' imply "g is the ''only'' antiderivative of f".  (6 m/s)t is ''an'' antiderivative of 6 m/s and thus it is correct that 6 m/s is the derivative of (6 m/s)t. It's also the derivative of (6 m/s)t + 3 m; that doesn't mean it's suddenly not the derivative of (6 m/s)t anymore. There's nothing wrong with that. For clarity, a [[constant of integration]] is not ''part'' of an [[antiderivative]], but rather provides a convenient way to denote the ''set'' of all antiderivatives.--[[User:Jasper Deng|Jasper Deng]] [[User talk:Jasper Deng|(talk)]] 21:01, 5 April 2024 (UTC)
::Right, thank you for this [[Special:Contributions/2.36.106.75|2.36.106.75]] ([[User talk:2.36.106.75|talk]]) 18:08, 13 April 2024 (UTC)