(III) (a) A particle moves in three-dimensions with constant velocity, At t-0 th
ID: 1871059 • Letter: #
Question
(III) (a) A particle moves in three-dimensions with constant velocity, At t-0 the particle is found at the origin, o (0,0,0) (2, -3, 4) B/s (i) Determine the speed (magnitude of the velocity) of the particle rna (ii) Determine the position of the particle at the instant t = 2 s. (iii) Determine where the particle crosses the plane z = 10 n. (b) A particle moves in three-d with constant acceleration, ao = (12,-12, 6) /82. At t = 0, the particle is instantaneously at rest,= (0,0,0) cm/s, at ro-(0, 24 , 17) (i) Determine the magnitude of the acceleration. (i) Determine the velocity of the particle at the instant t1s (iii) Determine the position of the particle at the instant t = 1 s. (iv) Determine where the particle crosses the n-plane, i.e., y = 0, after 1 = 0. Page 3 of 4Explanation / Answer
III (a) (i) |v| = sqrt(2^2 + 3^2 + 4^2) = 5.39 m/s
(ii) r = v t = (4, -6 , 8 ) m
(iii) z = 10 m = 4 t
t = 10/4 = 2.5 sec
(B) |a| = sqrt(12^2 + 12^2 + 6^2) = 18 cm/s^2
(ii) v = v0 + a t
v = (0, 0, 0) + 1(12, - 12, 6)
v = (12, -12, 6) cm/s
(iii) r = r0 + v0 t + a t^2 /2
r = (0.,24, 17) + (0, 0, 0) + (1^2 / 2 )(12, -12, 6)
r = (6 , 18, 20) cm
(iV) y = 0
0 = 24 + (0 x t) + (-12 x t^2 /2)
0 = 24 - 6 t^2
t = 2 sec
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.