The position vector of a body, with respect to the origin, is given by (r = 4ti + (12 – 3t)j) at any time t seconds.
(a) Find the velocity of the body ;
(b) Calculate the magnitude of the displacement between t = 0 and t = 5.
Explanation
(r = 4t i + (12 – 3t)j)
(a) (v = frac{mathrm d r}{mathrm d t} = 4i – 3j)
(b) When t = 0, r = 0i + 12j = 12j.
When t = 5, r = 20i – 3j.
Displacement = (r_{t = 5} – r_{t = 0})
= (20i – 3j – 12j)
= (20i – 15j)
(|Disp| = sqrt{20^{2} + 15^{2}} = sqrt{400 + 225})
= (sqrt{625} = 25m)