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A particle starts with origin at t=0 with velocity 5i m/s and moves in x-y plane under action of force which produces a constant accleration of (3i + 2j) m/s^2. What is the y coordinate when x coordinate is 84m? What is the speed of the particle at this time?

Saras , 9 Years ago
Grade 11
anser 1 Answers
Riddhish Bhalodia

Last Activity: 9 Years ago

As it is the case of constant acceleration we can use the equations of kinematics
\bar{u} = 5i, \bar{a} = 3i+2j
and the displacement required is after time t
\bas{S} = 84i + yj
using the second equation of kinematics is
\bas{S} = \bar{u}t + 0.5\bar{a}t^2 = (5t + 1.5t^2)i + t^2j
thus comparing the x coordinates we have a quadratic equation as
3t^2+10t -168 = 0
whose roots are 6, -28/3 and the meaning value of time is 6 seconds
Thus t = 6
Now using this in the y coordinate from the equation we have y = 36m
To find the final speed we find the velocity first
\bar{v} = \bar{u} + \bar{a}t = 23i + 12j
thus the speed = |v| = 25.94

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