At t = 0, a particle starts from rest at 𝓍 = 0, y = 0 and moves in the xy plane with an acceleration $\vec{a}=(4.0\hat{i}+3.0\hat{j}){\text{ m/s}}^2$. Determine the 𝓍 and y components of velocity, the speed of the particle, and the position of the particle, all as a function of time. Evaluate all the above at t = 2.0 s.

A skier is accelerating down a 30.0° hill at 1.80 m/s² (Fig. 3–42). How long will it take her to reach the bottom of the hill, assuming she starts from rest and accelerates uniformly, if the elevation change is 125 m? 

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A batter hits a fly ball which leaves the bat 0.90 m above the ground at an angle of 64° with an initial speed of 28 m/s heading toward centerfield. Ignore air resistance. The ball is caught by the centerfielder who, starting at a distance of 105 m from home plate just as the ball was hit, runs straight toward home plate at a constant speed and makes the catch at ground level. Find his speed.

Two masses are connected by a string as shown in Fig. 8–35. Mass m_A = 3.5 kg rests on a frictionless inclined plane, while m_B = 5.0 kg is initially held at a height of h = 0.75 m above the floor. If the masses were initially at rest, use the kinematic equations (Eqs. 2–12) to find their velocity just before m_B hits the floor.

Is this particle curving upward, curving downward, or moving in a straight line?

A survey drone has just completed a scan at x,y coordinates (57m, 8m) at t=0. It needs to return to a lab located at (-115, 72) m. If its initial velocity is 16m/s in the +y-direction, and it has only 18s of battery life remaining, what constant acceleration (magnitude and direction) does it need to reach the lab?