Suppose the position vector for a particle is given as a function of time...

Question

by r(t) = x(t)î + y(t)ĵ, with x(t) = at + b and y(t) = ct² + d, where a = 2.00 m/s, b = 1.30 m, c = 0.132 m/s², and d = 1.20 m.

(a) Calculate the average velocity during the time interval from t = 2.05 s to t = 3.95 s.

(b) Determine the velocity at t = 2.05 s.

(c) Determine the speed at t = 2.05 s.

Answer 1

a) The average velocity vector v = (r₂ - r₁) / (t₂ - t₁). You can do the subtraction by components and r_i is the position vector at t_i.

b) v = dx/dt (ihat) + dy/dt (jhat) evaluated at t = 2.05 s

c) speed is sqrt( (dx/dt)² + (dy/dt)² ) at t = 2.05 s