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Question

A particle starts from the origin at t = 0 s with a velocity of 10.0 ^j m/s and moves in the x-y plane with a constant acceleration of (8.0^i+2.0^j) m/s2.
(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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Solution

Given:
The initial velocity of particle is u=10^jm/s
The acceleration of the particle is a=8^i+2^j

(a)
The position of the particle at any instant is given by:
s=ut+12at2

x^i+y^j=4t2^i+(10t+t2)^j

Comparing the X and Y component of the position:
x=4t2
x=16t=2s

y=10t+t2
At t=2, y=24m

(b)
The speed of the particle at any instant is given by:
v=u+at
v=10^j+(8^i+2^j)2

v=14^j+16^i

|v|=142+162=21.26m/s



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