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1. To find k, differentiate the velocity equation to get the acceleration equation. Substitute t=2 and a=3 into the acceleration equation to get the value of k.
2. To get an expression for the displacement, Integrate the velocity equation to get the displacement equation. Don't forget to find constant (c) by substituting t=0 and s=0 . The reason why we substitute s=0 and t=0 is because the particles started moving from origin 0 m.
3. To find the distance traveled. First determine if the particle turn by finding time (t) when velocity =0. In this case t=-1/2 when v=o, there is no such thing as t=-1/2 i.e. negative time , so we can safely assume that the particle did not turn. Since the particle did not turn, the displacement = distance traveled, we substitute t=o into the displacement equation to get the distance of 16.4m

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