Physics with Calculus
Which expression gives the instantaneous velocity for a 2D2\(\text{D}\) position vector R→(t)\(\overrightarrow{R}\]\left\)(t\(\right\))?
A particle moves in the plane with position vector R→(t)=(2t4−3t)i^+(7−t2)j^\(\overrightarrow{R}\]\left\)(t\(\right\))=\(\left\)(2t^4-3t\(\right\))\(\hat{i}\)+\(\left\)(7-t^2\(\right\))\(\hat{j}\). What is its instantaneous velocity vector V→(t)\(\overrightarrow{V}\]\left\)(t\(\right\))?
For the vector velocity function V→(t)=(6t−4)i^+9t2j^\(\overrightarrow{V}\]\left\)(t\(\right\))=\(\left\)(6t-4\(\right\))\(\hat{i}\)+9t^2\(\hat{j}\), which antiderivative could represent a position function before applying any initial condition?
A rescue boat has velocity V→(t)=(t2−4t)i^+(6−3t)j^\(\overrightarrow{V}\]\left\)(t\(\right\))=\(\left\)(t^2-4t\(\right\))\(\hat{i}\)+\(\left\)(6-3t\(\right\))\(\hat{j}\) for 1≤t≤31 ≤ t ≤ 3. What is the displacement from t=1t = 1 to t=3t = 3?
Why is no constant of integration added when computing displacement from t1t_1 to t2t_2 using a definite integral of velocity?
