SAMPLE PROBLEM 2 4 A particle moves in the xy plane so that its x and y coordinates vary with time according to x t At Bt and y

Question

SAMPLE PROBLEM 2 4 A particle moves in the xy plane so that its x and y coordinates vary with time according to x t At Bt and y t Ct2 D where A 1 00 m s B 32 0 m s C 5 0 m s and D 12 0 m Find the posi tion velocity and acceleration of the particle when t 3 s Solution The position is given by Eq 2 5 with the expressions given for x t and y t Substitute for A B C D and t then find out r as F Now x y At Bt i Ct D Result The velocity components are found from Eq 2 12 dx dt ax dy dt Substitute for A B C D and t then find out v as v vy The components of the acceleration are ay V x Vy dvx dt dvy dt Position vector r d dt d dt At Bt 3At B dt i d Ct D 2Ct dt At t 3 s the acceleration is Substitute for A B C and t then find out a as 3At B 6At 2Ct 2C i a a a m s i m s j

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