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The initial velocity of an object is vec...

The initial velocity of an object is `vecu = 5hati + 10hatj m//s`. Its constant acceleration is `veca = 2hati+ 3 hatj m//s^2`. Determine the velocity and the displacement after 5 s.

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`vecv =vecu + veca t =(5hati + 10hatj)+(2hati + 3hatj)(5)=15hati + 25hatj`
`:. v= sqrt(v_x^2+v_y^2)`
`= sqrt(15^2 + 25^2) = sqrt(225 +625) = sqrt850`
`= 29.15 m//s`
Direction of `vecv " with x-axis is " tan^(-1)( v_y/v_x ) = tan^(-1)`
`(25/15) =tan^(-1) (1.667) = 59^@`
`vecs = vecu t+ 1/2 veca t^2`
`=(5hati +10 hatj)(5)+1/2 (2hati + 3hatj)5^2`
`= 50hati +(87.5)hatj`
`:. S = sqrt(s_x^2+s_y^2)= sqrt(50^2 +87.5^2)`
`= sqrt(2500+ 7656.25)`
`= sqrt(10156.25) = 100.78 m`
at `tan^(-1)(187.5)/50 = 60^@15.` with X-axis.
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