Suppose that the position vector for a particle is given as a function of time by vector r (t) = x(t)i hat bold + y(t)j hat bold, with x(t) = at + b and y(t) = ct2 + d, where a = 1.80 m/s, b = 1.20 m, c = 0.130 m/s2, and d = 1.08 m.

(a) Calculate the average velocity during the time interval from t = 1.85 s to t = 4.05 s.

(b) Determine the velocity at t = 1.85 s.

(c) Determine the speed at t = 1.85 s.

v(t)=dr(t)/dt= a i + 2ct j

a)average velocity=(x2-x1)/(4.05-1.85) i + (y2-y1)/(4.05-1.85) j

=(9.09-4.53)/2.2 i +(3.212325-1.524925)/2.2 j

=2.073 i+0.767 j

b) velocity=1.8 i +2*0.13*1.85 j=1.8 i +0.481 j

c)speed=sqrt(1.8^2+0.481^2)=1,863 m/s.