The motion equation of a particle moving in the oxy plane is r = 2Ti + (19-2t) J (SI system). Find: (1) the trajectory equation of the particle, (2) the position, velocity and acceleration of the object when T1 = 2S, (3) the average velocity from T1 = 2S to T2 = 3S

The motion equation of a particle moving in the oxy plane is r = 2Ti + (19-2t) J (SI system). Find: (1) the trajectory equation of the particle, (2) the position, velocity and acceleration of the object when T1 = 2S, (3) the average velocity from T1 = 2S to T2 = 3S

(1) X = 2T, y = 19-2t, equation of motion: y = 19-x
(2)r=2ti+(19-2t)j,v=dr/dt=2i-2j,a=dv/dt=0
When T1 = 2S, r = 4I + 15J, v = 2i-2j, a = 0
(3) It is known from (2) that the particle moves in a straight line with uniform velocity, v = 2i-2j, v = 2 √ 2

Find the quadratic equation of one variable so that its two roots are three times of the two roots of the equation 3x square + 5x-2 =

3x ^ 2 + 5x-2 = 0 let two of the above equations be X1 and X2 respectively. From the relationship between root and coefficient, we get X1 + x2 = - 5 / 3x1 * x2 = - 2 / 3. Let two of the new equations be 3x1 and 3x2, then 3x1 + 3x2 = 3 (x1 + x2) = 3 * (- 5 / 3) = - 53x1 * 3x2 = 9x1 * x2 = 9 * (- 2 / 3) = - 6, so the new univariate quadratic equation is y ^ 2 + 5y-6 = 0

Find the complex solution to the equation x ^ 3 = 8

2, - 1 + radical 3 I, - 1 - radical 3 I
method:
Let's draw the radius of the other two points in the coordinate system of 3 points