TEST AU12

1.  ( 40 points) A car travels down a lonely road at constant velocity 20.0  m/s. Suddenly,  at t = 0,  the driver sees a deer in the road. After a  reaction time tR  = 1.5 seconds,  the driver steps on the brakes and the car then decelerates (slows down)  at constant acceleration with magnitude 4.00 m/s2 before coming to rest at time tf. Below is the velocity v vs. time t graph of the car’s motion.

 


(a)  (8 points)   What is the time  tf  when the car finally comes to rest? 
(b)  (5  points)  What is the car’s  displacement (in m) at t = 1.0 seconds?

(c)  (5  points)  What is the car’s displacement  (in m) at t = 4.0 seconds?
(d)  (5  points)  At what time t is the car’s instantaneous velocity v =
                          5.0 m/s?
(e)  (4 points)   At what time t  is the car ‘s instantaneous velocity  v =
                         10.0 m/s?
(f)  (5 points)   What is the car’s
average velocity (in m/s)  in the time interval between  tR  and  tf   (when the car is slowing down)?
(g) (8 points)   What is the total displacement (i.e. stopping distance in meters)  between t = 0 and t = tf  .

 

 

 

2. (40 points) A ball is thrown downward  with initial speed 2.00 m/s toward a lake from a diving board that is 11 m above the surface of the water. While the ball is in the air, it is in free fall with acceleration of magnitude g directed downward.  After the ball hits the water, it slows down and sinks downward with an upward acceleration of  magnitude 3.00 m/s2 .  

 

(a) (20 points) What is the ball’s speed just before it hits the water surface?

 

(b) (20 points) What is the maximum  depth D below the water surface  reached by the  decelerating   ball?

 





 

 

3.  ( 40 points) A place kicker kicks a football from a point a horizontal distance of 37.00 m from the goal.   When kicked (at t = 0), the ball leaves  the ground (at y = 0) with  speed 21.00 m/s at an angle of
51 degrees
with the horizontal.  Below is a schematic of the ball’s path and the ball at the start of its motion.  The goal location is horizontally 37.00 m to the right of the ball shown by the dot   .

 

(a) (24 points) What is the vertical  height h of the ball when it  passes  the goal?  
(b) (8 points) What is the y-component of velocity Vy when the ball passes the goal?
(c) (4 points)  What is the x-component of velocity Vx when the ball passes the goal? Explain.
(d) (4 points) Using the Pythagorean Theorem, find the speed of the ball when it passes over the goal?


4. (a) (20) In the diagram below,  has magnitude 3.6 m  with the direction shown.  has magnitude 3.0 m and points in the 3rd quadrant with direction shown.  Write each vector  component  in the blanks provided.  Show work  in spaces below and next pages.
   (b) (11) Compute the magnitude  of the vector sum. Show work  in spaces below and next pages .
   (c) (9) Find the  direction of the vector sum  by doing the following:
      (i) Show the direction by drawing this vector sum in the correct quadrant on the blank axes provided on next page.
      (ii) Calculate the related (reference) angle  the vector makes with the  x-axis. Show this angle in sketch, with work.

Ax  = __________________ Ay = ______________________


Bx  = _________________    By = _______________________

 

 

 

 


5. ( 10 points) You swing a 2.2 kg stone in a circle of radius r = 75 cm. At what speed v should you swing it so its centripetal acceleration has magnitude aC = 8.0 m/s2?

 

  

Short Answers. Multiple choice: Mark your scantron with a #2 pencil.  

1. It is possible to be moving and have zero acceleration.
(a) True (b) False

 

2. An object moves in a straight line at constant speed. The net force on  the object must  be (a) not zero  (b) zero  (c)  infinite (d) none of the above

3. When the velocity of an object is zero, the object is
(a) moving  (b) at rest


4.  When the velocity and acceleration point in opposite directions, the speed of the object  (a) increases (b) decreases (c) is constant

 

5. Assume no air resistance. An object is released from rest above the ground. As the object  moves down, the acceleration magnitude is 
(a) 0 (b) 9.8 m/s2

6. Assume no air resistance. An object is thrown downward from  above the ground.  As the object moves down, the acceleration magnitude is
(a) 0  (b) more than 9.8 m/s2  (c)  9.8 m/s2 

7.  Assume no air resistance. An object is thrown upward  from  above the ground.  As the object rises, its acceleration magnitude 
(a) decreases (b) increases (c) is constant

 

8. The slope of a line connecting two points on a position  (x) versus time (t) graph gives (a) the average  velocity (b) the instantaneous velocity.

 

9. The slope of a tangent line at a given time on a  position (x) versus time (t) graph gives (a) the average  velocity (b) the instantaneous velocity.

10. Assume no air resistance. A stone is thrown up. As the stone rises, its  speed  (a) increases   (b) decreases. 

 

11. Assume no air resistance. A stone is thrown up. What is its speed at the highest point? (a)  the same as the initial  speed   (b) 0  

12. When the velocity of an object is zero, the object’s acceleration must be zero.   (a) True  (b) False