Determine the parametric equations of the position of a particle with constant v

Question

Determine the parametric equations of the position of a particle with constant velocity that follows a straight line path on the plane if it starts at the point P(- 9, - 7) and after one second it is at the point Q(- 5,1). X(t) = y(t)= What is the speed of the particle? Speed = Determine the parametric equations of the position of a particle with constant velocity that follows a straight line path in space if it starts at the point R(- 3,3,-1) and after one second it is at the point S(- 8,4,0). x(t) = y(t) = z(t) = What is the speed of the particle? speed =

Explanation / Answer

solution:

The parametric representation of a line says that if we are Given two points (x1, y1) and (x2, y2), the point (x, y) is on the line determined by (x1, y1) and (x2, y2) if and only if there is a real number t such that

x = (1 - t)x1 + tx2,

and

y = (1 - t)y1 + ty2

now here

(x1,y1)= (-9,-7)

(x2,y2)=(-5,1)

hence

x = (1 - t)(-9) + t(-5)

x=4t-9

and

y = (1 - t)(-7) + t(1)

y=8t-7

hence velocity is.

v=(4i+8j)

as

vx=dx/dt

vy=dy/dt

2) using same method doing this part

x = (1 - t)(-3) + t(-8)

x=-5t-3

and

y = (1 - t)(3) + t(4)

y=3+t

z= (1 - t)(-1) + t(0)

z=t-1

hence velocity as calculated in above case

v=(5i+1j+1k)

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