A particle moves in two dimensional space where i and į are unit vectors in the x and y directions respectively. At time t seconds its displacement from the origin is given by r = (6t - 4t²)i + 2t j where all lengths are measured in metres. (i) Write down the particle's velocity vector in component form. (ii) Find the speed of the particle when t = 2.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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A particle moves in two dimensional space where i and j are unit vectors in the x and y directions
respectively. At time t seconds its displacement from the origin is given by r = (6t - 4t²)i + 2t j
where all lengths are measured in metres.
(i) Write down the particle's velocity vector in component form.
(ii) Find the speed of the particle when t = 2.
(iii) Show that the equation of the path of the particle is x =
3y - y².
Transcribed Image Text:A particle moves in two dimensional space where i and j are unit vectors in the x and y directions respectively. At time t seconds its displacement from the origin is given by r = (6t - 4t²)i + 2t j where all lengths are measured in metres. (i) Write down the particle's velocity vector in component form. (ii) Find the speed of the particle when t = 2. (iii) Show that the equation of the path of the particle is x = 3y - y².
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