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**A car rolling down a hill with an inclination [tex]\alpha[/tex] with the horizon experiences an acceleration [tex]a = gsin(\alpha)[/tex] along the surface of the hill. Here [tex]g = 9.81 m/s^2[/tex]. The car is released from rest at the time t**

_{0}= 0sa) Find the position s and the velocity v of the car along the hill after a time t.

b)

*We will now introduce a reference system S oriented with the x-axis in the horizontal direction and the y-axis in the vertical direction (the direction gravity isacting). The car starts in the position x = 0 m, y = h, where h is the height of the car, and the car moves in the positive x-direction.*

Find the position [tex]\vec{r(t)}[/tex] and the velocity [tex]\vec{v(t)}[/tex] of the car along the hill after a time t

**What is the**

*difference*in solving a) and b)? As the velocity and position in a) are scalars, but vectors in b)