Question

The position ModifyingAbove r With right-arrow of a particle moving in an xy plane is given by ModifyingAbove r With right-arrow equals left-parenthesis 4 t cubed minus 3 t right-parenthesis ModifyingAbove i With caret plus left-parenthesis 6 minus 2 t Superscript 4 Baseline right-parenthesis ModifyingAbove j With caret with ModifyingAbove r With right-arrow in meters and t in seconds.

In unit-vector notation, calculate

(a)ModifyingAbove r With right-arrow,

(b)v Overscript right-arrow EndScripts, and

(c)a Overscript right-arrow EndScripts for t = 2 s.

(d) What is the angle between the positive direction of the x axis and a line tangent to the particle's path at t = 2 s? Give your answer in the range of (-180o; 180o).

The postion of a particle moving in an xy plane is given by (4t3 - 31)7+ (6 - 2t4) with F in meters and t in seconds. In unit-vector notation, calculate The position r of a particle moving in an xy plane is given by r =(4"-30i+( (a) , (b) ,and (c) a for (a) (b) V,and (c) fort-2 s. (d) What is the angle between the positive direction of the x axis and a line tangent to the particle's path at t- 2 s? Give your answer in the range of (-180°; 1809). r = ( 4t _ 3 t), + (6-21") j with r in meters and t in seconds. In unit-vector notation, calculate → (a) NumberV Units 'm (b) Numberi UnitsTm/s (c) Number UnitsT m/s 2 (d) Number Units (degrees

Answer 1

a) The position at (t-2s) is given by -(26:-26).) m b) The velocity at (t-2s) is given by., dr d dt dt v 12x(2)-3 -= (45 i-64j) m/s c) The accelaration at (t-2s) is given by dv d 12t-31 dt dt a -(24t)i (24t ā-(24x2 а:(481-96))ms ) i-(24 x (2).)j