1) In a test run, a certain car accelerates uniformly from zero to 18.6 m/s in 2.25 s.(a) What is the magnitude of the car's acceleration? (b) How long does it take the car to change its speed from 9.30 m/s to 18.6 m/s? (c) Will doubling the time always double the change in speed? YesNo Why?

2) A ball is thrown directly downward with an initial speed of 8.05 m/s, from a height of 30.2 m. After what time interval does it strike the ground?

3) A model rocket is launched straight upward with an initial speed of 49.0 m/s. It accelerates with a constant upward acceleration of 1.00 m/s² until its engines stop at an altitude of 200 m.

(a) What can you say about the motion of the rocket after its engines stop?

(b) What is the maximum height reached by the rocket? (c) How long after liftoff does the rocket reach its maximum height? (d) How long is the rocket in the air?

4)A baseball is hit so that it travels straight upward after being struck by the bat. A fan observes that it takes 2.90 s for the ball to reach its maximum height.

(a) Find the ball's initial velocity. (b) Find the height it reaches.

5) Emily challenges her husband, David, to catch a $1 bill as follows. She holds the bill vertically, with the center of the bill between David's index finger and thumb. David must catch the bill after Emily releases it without moving his hand downward. If his reaction time is 0.2 s, will he succeed? YesNoand why?

6) Vector A has a magnitude of30units and points in the positivey-direction.When vector B is added to A, the resultant vector A+B points in the negativey-directionwith a magnitude of15units.

Find the magnitude and direction of B.

7) A force F₁ of magnitude5.80units acts on an object at the origin in a direction=47.0above the positivex-axis. A second force F₂ of magnitude5.00 unitsacts on the object in the direction of the positivey-axis.

Find graphically the magnitude and direction of the resultant force F₁+F₂.

8) The magnitude of vector A is29.5units and points in the direction350counterclockwise from the positivex-axis.Calculate thex-andy-componentsof this vector.

9) A figure skater glides along a circular path of radius 4.38 m.

(a) If she coasts around one half of the circle, find the magnitude of the displacement vector.

(b) If she coasts around one half of the circle, find what distance she skated.

(c) What is the magnitude of the displacement if she skates all the way around the circle?

10) A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of v₀=21.5m/s.

The cliff ish=42.0mabove a flat, horizontal beach.

(a) What are the coordinates of the initial position of the stone?

(b) What are the components of the initial velocity?

(c) Write the equations for the x- and y-components of the velocity of the stone with time. (Use the following as necessary: t. Let the variable t be measured in seconds. Do not include units in your answer.)

(d) Write the equations for the position of the stone with time, using the coordinates in the figure. (Use the following as necessary: t. Let the variable t be measured in seconds. Do not state units in your answer.)

(e) How long after being released does the stone strike the beach below the cliff?

(f) With what speed and angle of impact does the stone land?

11) A playground is on the flat roof of a city school, h_b = 5.10 m above the street below. The vertical wall of the building is h = 6.30 m high, to form a 1.2-m-high railing around the playground. A ball has fallen to the street below, and a passerby returns it by launching it at an angle of = 53.0 above the horizontal at a point d = 24.0 m from the base of the building wall. The ball takes 2.20 s to reach a point vertically above the wall.

(b) Find the vertical distance by which the ball clears the wall.

(c) Find the horizontal distance from the wall to the point on the roof where the ball lands.

12) An airplane flies 200 km due west from city A to city B and then 330 km in the direction of 33.0 north of west from city B to city C.

(a) In straight-line distance, how far is city C from city A? (b) Relative to city A, in what direction is city C? (c) Why is the answer only approximately correct?