2) A particle moves on the xy-plane, starting from the origin at t = 0 with an i

Question

2) A particle moves on the xy-plane, starting from the origin at t = 0 with an initial velocity having an x component of 18 m/s and a y component of -11 m/s. The particle experiences an acceleration that is in the x direction given by ax = 6.2 m/s2. a) Determine the total velocity vector at any time. b) Calculate the velocity and speed of the particle at t = 5.0 s and the angle the velocity vector makes with the x-axis. c) Determine the x and y coordinates of the particle at any time t and its position vector at this time.

Explanation / Answer

(a) v = u + at

u = 18 i - 11 j

a = 6.2i

Hence, v = (18 + 6.2t)i - 11j

(b) At t = 5s,

v = (18 + 6.2*5)i - 11j = 49i - 11j

Speed = sqrt(492 + 112) = 50.22 m/s

(c)

s = ut + (1/2)at2

s = (18i - 11j)t + (1/2)(6.2i)t2 = (18t + 3.1t2)i - (11t)j ----- position vector.

x-component -   (18t + 3.1t2)

y-component - (11t)

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