When determining parametric equations for the position of a particle from its…

MATHEMATICS · Single correct · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

When determining parametric equations for the position of a particle from its velocity components dxdt=f(t)\dfrac{dx}{dt}=f(t) and dydt=g(t)\dfrac{dy}{dt}=g(t), knowing that the particle passes through the point (3,−1)(3,-1) at t=2t=2 primarily enables a student to do which of the following? (a) Establish the constants of integration that arise after integrating ff and gg (b) Choose a specific antiderivative formula for ff and gg (for example, whether to write +C+C or omit it) (c) Compute the displacement vector ⟨x(2)−x(0), y(2)−y(0)⟩\langle x(2)-x(0),\,y(2)-y(0)\rangle by evaluating definite integrals of ff and gg from 00 to 22 (d) Determine the slope of the particle’s path at t=2t=2 by using dydx=g(2)f(2)\dfrac{dy}{dx}=\dfrac{g(2)}{f(2)}

Related theory

Browse the problem library