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(-6, 6) and after one second it is at the point Q(8, 8). What is the speed of the particle? 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(2, -8, 4) and after one second it is at the point S(9, 2, -2). What is the speed of the particle?

Explanation / Answer

1)P=(-6,6), Q=(8,8)

x(t)=-6+(8-(-6))t =-6+14t

y(t)=6+(8-6)t =6+2t

r(t)=<-6+14t ,6+2t>

v(t)=r '(t)=<14,2>

speed =|v(t)|=(142+22)

speed =200

speed =102

speed =14.14

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x=2+(9-2)t =2+7t

y=-8+(2-(-8))t =-8+10t

z=4+(-2-4)t =4-6t

speed =(72+102+(-6)2)

speed =(49+100+36)

speed=13.6

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