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Finding Average Velocity

A particle st...

Question

A particle statrs from the origin at t=0 with the velocity 5i^m/s and moves in x-y plane under the action of the force which produces a constant acceleration of (4i^ + 2j^) m/ss
a) what is the y coordinate of the particle at an instant when its x coordinate is 84 m?
b) what is the speed of the particle at this time?

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Solution

$i n i t i a l v e l o c i t y i n x d i r e c t i o n = 5 m / s a c c e l e r a t i o n i n x d i r e c t i o n = 4 m / s^{2} t i m e t a k e n t o t r a v e l t h e d i s \tan c e 84 m i n x d i r e c t i o n i s t . s = u t + \frac{1}{2} a t^{2} 84 = 5 t + \frac{1}{2} 4 t^{2} 2 t^{2} + 5 t - 84 = 0 - - - (1) a c c e l e r a t i o n i n y d i r e c t i o n i s 2 m / s^{2} i n i t i a l; v e l o c i t y i n y d i r e c t i o n = 0 d i s \tan c e t r a v e l i n t i m e t i n y d i r e c t i o n i s g i v e n b y : y = \frac{1}{2} \times 2 \times t^{2} y = t^{2} f r o m e q u a t i o n (1) w e c a n c a l c u l a t e t h e v a l u e o f t a n d t h e n w e c a n f i n d t h e v a l u e o f y s p e e d o f t h e p a r t i c l e i n x d i r e c t i o n = v = u + a t v_{x} = 5 + 4 t v_{y} = 0 + 2 t v = \sqrt{{v_{x}}^{2} + {v_{y}}^{2}}$

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D meters

D

A particle starts from the origin at t = 0 s with a velocity of and moves in the x-y plane with a constant acceleration of .

(a) At what time is the x-coordinate of the particle 16 m? What is the y-coordinate of the particle at that time?

(b) What is the speed of the particle at the time?

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