A particle moves in the plane with velocity vector for
MATHEMATICS · Multi-part · AP · Calculus BC · Applications of Integration · Applications of Integration
Problem
A particle moves in the plane with velocity vector v(t)=⟨3t2,4t⟩ for 0≤t≤2, where t is measured in seconds and the components are in meters per second.
(a) Write an expression for the particle’s speed s(t).
(b) Evaluate the definite integral that gives the total distance the particle travels from t=0 to t=2. Include units in your answer.
(c) Compute the displacement vector of the particle over the same time interval and determine its magnitude.
(d) Compare the magnitude of the displacement found in part (c) to the total distance traveled found in part (b). Explain what your comparison indicates about the particle’s path.