In this question the unit vectors i and j are in the directions east and north respectively. A particle R of mass 2kg is moving on a smooth horizontal surface under the action of a single horizontal force FN. At time t seconds, the velocity vms of R, relative to a fixed origin O, is given by v = (pr -31)i+ (8t+q)j, where p and q are constants and p< 0. (a) Given that when t = 0.5 the magnitude of F is 20, find the value of p.

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Chapter1: Units, Trigonometry. And Vectors
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In this question the unit vectors i and j are in the directions east and north respectively.
A particle R of mass 2kg is moving on a smooth horizontal surface under the action of a single
horizontal force FN. At time t seconds, the velocity vms of R, relative to a fixed origin O, is
given by v = (pr -31)i + (81 +q)j, where p and q are constants and p<0.
(a) Given that when t= 0.5 the magnitude of F is 20, find the value of p.
When t= 0, R is at the point with position vector (2i – 3j) m.
(b) Find, in terms of q, an expression for the displacement vector of R at time t.
When t = 1, R is at a point on the line L, where L passes through O and the point with position
vector 2i - 8j.
(c) Find the value of q.
Transcribed Image Text:In this question the unit vectors i and j are in the directions east and north respectively. A particle R of mass 2kg is moving on a smooth horizontal surface under the action of a single horizontal force FN. At time t seconds, the velocity vms of R, relative to a fixed origin O, is given by v = (pr -31)i + (81 +q)j, where p and q are constants and p<0. (a) Given that when t= 0.5 the magnitude of F is 20, find the value of p. When t= 0, R is at the point with position vector (2i – 3j) m. (b) Find, in terms of q, an expression for the displacement vector of R at time t. When t = 1, R is at a point on the line L, where L passes through O and the point with position vector 2i - 8j. (c) Find the value of q.
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