Physics with Calculus
When finding a position vector from a velocity vector using an indefinite integral, what must be included?
A rover moves with velocity V→(t)=(3t2−2)i^+(4t+1)j^\(\overrightarrow{V}\]\left\)(t\(\right\))=\(\left\)(3t^2-2\(\right\))\(\hat{i}\)+\(\left\)(4t+1\(\right\))\(\hat{j}\). What is its displacement from t=0t = 0 to t=2t = 2?
A submersible follows velocity V→(t)=(3t2−6t)i^+(4t+2)j^\(\overrightarrow{V}\]\left\)(t\(\right\))=\(\left\)(3t^2-6t\(\right\))\(\hat{i}\)+\(\left\)(4t+2\(\right\))\(\hat{j}\). If R→(2)=5i^+j^\(\overrightarrow{R}\]\left\)(2\(\right\))=5\(\hat{i}\)+\(\hat{j}\), what is its position vector R→(t)\(\overrightarrow{R}\]\left\)(t\(\right\))?
