A particle travels along a piecewise-defined path

PHYSICS · Multi-part · AP · Physics C: Mechanics · Kinematics · Kinematics

Problem

A particle travels along a piecewise-defined path. For 0≤t≤10\le t\le 1, its position is r1(t)=⟨t, t2, 0⟩\mathbf r_{1}(t)=\langle t,\,t^{2},\,0\rangle. For 1≤t≤31\le t\le 3, its position is r2(t)=⟨1, t, t−1⟩\mathbf r_{2}(t)=\langle 1,\,t,\,t-1\rangle. (a) Find the exact length of the first segment of the journey (0≤t≤10\le t\le 1). (b) Find the exact length of the second segment of the journey (1≤t≤31\le t\le 3). (c) Determine the total distance traveled by the particle during the entire time interval 0≤t≤30\le t\le 3. Express your answer in simplest exact form.

Related theory

Browse the problem library