What is the speed of the particle? speed = What is the speed of the particle? sp

Question

What is the speed of the particle?
speed =

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 on the plane if it starts at the point z (t ) = What is the speed of the particle? speed = y (t ) = x (t ) = S( 10, -9, 8 ) . R( -4, 8, 9 ) and after one second it is at the point 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 x (t ) = Q( 4, 8 ) . P( 5, -4 ) and after one second it is at the point

Explanation / Answer

1.
r(t) = P + (Q-P) t

x(t) = 5 + ( 4-5) t = 5 - t

y(t) = -4 + ( 8-(-4)) t = -4+ 12 t

speed = sqrt ( x'(t)^2 + y'(t) ^2 )

speed = sqrt ( 1^2 + 12^2 ) = sqrt 145

2.

r(t) = R + (S-R) t

x(t) = -4 + ( 10-(-4)) t =-4 +14 t

y(t) = 8 + ( -9-8) t = 8-17t

z(t) =9 + ( 8-9) t =9 -t

speed = sqrt ( x'(t)^2 + y'(t) ^2+z'(t)^2 )

speed = sqrt ( 14^2 + 17^2 +1^2 ) = sqrt 486

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