SparkNotes: Review of Kinematics: Kinematics Multiple Choice Test

1. Two birds are flying directly towards each other at the same speed If the first bird is flying at a velocity v, what is the the velocity of the second bird?

(A) v

(B) - v

(C) 2v

(D) Impossible to determine

2. A United Airlines jet is flying at 300 km/hr, while an Air France Concord is speeding along at 1200 km/hr Both airplanes are flying at the same altitude If each aircraft experiences problems with an unruly passenger, and they both decide simultaneously to push the passenger out the door, which of the unruly passengers will hit the earth first? (Ignore air resistance)

(A) The Air France passenger

(B) The United Airlines passenger

(C) Neither They will both hit the ground at the same time

(D) Impossible to determine The answer depends on which passenger is heavier

3. Assuming the airplanes in the previous problem continue to travel at the same velocity after ejecting their respective passengers, where will the passengers land with respect to their aircraft's path?

(A) When they hit the ground, they will be directly beneath the airplane they fell from

(B) When they hit the ground, they will be directly beneath the spot at which the airplane threw them out

(C) They will be in front of the aircraft they fell from

(D) It depends on which plane the passenger fell from

4. The velocity function is all of the following EXCEPT

(A) A function of time

(B) The derivative of the position function

(C) A function which gives the velocity of an object at any point in time

(D) None of the above

5. A police officer living on a planet with no air resistance drops a pair of handcuffs and a handkerchief from the same height at the same time Which one will reach the ground first?

(A) The handkerchief

(B) The handcuffs

(C) They will both hit the ground at the same time

(D) The answer depends on how far above the ground they were when he dropped them

6. What kind of function is an acceleration function describing one-dimensional motion?

(A) A scalar-valued function

(B) A vector-valued function

(C) There is no such thing as acceleration in one dimension

(D) A constant function

7. In general, the acceleration of objects due to the earth's gravitational pull is

(A) constant

(B) 98 m/s²

(C) smaller if the object is further away

(D) greater if the object is further away

8. Kinematics is concerned with

(A) understanding why objects move the way they do

(B) describing the movement of objects

(C) action at a distance

(D) None of the above

9. A raindrop on a drizzly day takes one minute from the time it leaves the cloud until it hits your umbrella, 3 miles below The average velocity of the raindrop on its journey is

(A) 3 miles/hr

(B) 60 miles/hr

(C) 180 miles/hr

(D) Impossible to determine because the raindrop accelerates due to gravity

10. The average velocity and the instantaneous velocity of an object will be the same if

(A) the object's speed is constant

(B) the object's acceleration is zero

(C) the object's velocity is always positive

(D) They are never the same

11. A car traveling at constant velocity v suddenly brakes in an effort to keep from hitting a rabbit which is 8 ft away If the braking action causes a constant deceleration a, how long does it take for the car to come to a complete stop?

(A) t = va

(B) t = 8a/v

(C) t = 8a

(D) t = v/a

12. In the previous question, how far did the car travel as it was braking?

(A)

(B)

(C) 8av

(D)

a²

13. If the car from the last two questions had initially been traveling at a speed of 10 ft/s, and experienced (from the braking) a deceleration of 5 ft/s², would it have hit the rabbit which was 8 ft away? (Assume the rabbit was dazed and didn't move at all)

(A) yes

(B) no

(C) Impossible to determine without knowing the weight of the car

(D) Impossible to determine because the car can never reach a complete stop

14. Find the derivative of 2x⁵ +

x³ +

+ 5

(A) 10x⁵ + x² + 5

(B) 10x⁴ + x² -

(C) 10x⁴ + x² +

+ 5

(D) None of the above

15. Evaluate the derivative of x³ + x² + 5x at x = - 2

(A) -3

(B) -14

(C) -2

(D) None of the above

16. Find the velocity of an object described by the position function x(t) = 3x² +

at time t = - 1

(A) -2

(B) 5

(C) 2

(D) -5

17. Find the acceleration of an object described by the position function x(t) = 3x² +

at time t = - 1

(A) -8

(B) 5

(C) 18

(D) None of the above

For the following 5 questions, consider an object with position function x(t) =

(0, 0, - g)t² + (2, 3, 4)t + (5, 0, 1)

18. What is the magnitude of the initial (ie at t = 0) velocity vector?

(A) 5

(B)

(C)

(D) - g/2

19. What is the position of the object at time t = - 2?

(A) (1, - 6, - 2g - 7)

(B) -12

(C) (1, - 6, - 7)

(D) (0, 0, 0)

20. The object is moving

(A) in one dimension

(B) in two dimensions

(C) in three dimensions

(D) None of the above

21. What is the acceleration of this object at time t = 25?

(A) - g

(B) 25(0, 0, -

g)

(C)

g

(D) - (0, 0, g)

22. This equation might describe an object

(A) in free fall

(B) moving as a projectile

(C) bouncing straight up and down

(D) with changing acceleration

23. In creature-land, the measure of one's hardcoreness is directly correlated to how high one can jump Unfortunately, creatures cannot jump straight up, but must take a running start If creature A jumps with initial velocity vector (2, 2, 5), and creature B jumps with initial velocity vector (5, 4, 2) (where the z-direction points upwards), which creature is more hardcore?

(A) creature A

(B) creature B

(C) Both creatures are equally hardcore

(D) Impossible to determine without knowing the gravitational acceleration in creature-land

24. According to the previous question, which creature travels furthest during its jump?

(A) creature A

(B) creature B

(C) Both creatures land an equal distance away from their starting point

(D) Impossible to determine without knowing the gravitational acceleration in creature-land

25. Which function could describe the velocity of a ball being thrown horizontally off a fire escape?

(A) v(t) = -

(0, 0, g)t² + (0, v, 0)t + (0, 0, h)

(B) v(t) = - (0, 0, g)t + (v, 0, 0)t

(C) v(t) = - gt + vt

(D) v(t) = -

(0, 0, g)t + (0, 0, v)t

26. Phin and Wittgenstein are hanging out on the moon when they decide to have a contest to see who can shoot a bullet farther Both use identical guns Phin decides to shoot at a 60 degree angle, while Wittgenstein holds his gun at 45 degrees when shooting Whose bullet lands the furthest away?

(A) Phin's

(B) Wittgenstein's

(C) Both bullets land the same distance away

(D) Impossible to determine without knowing the acceleration due to gravity on the moon

27. The office of the Harvard Review of Philosophy is located approximately 10 ft below the earth's surface The acceleration due to gravity experienced by members working in this office is

(A) significantly greater than that of people on the earth's surface

(B) significantly smaller than that of people on the earth's surface

(C) approximately equal to that of people on the earth's surface

(D) exactly equal to that of people on the earth's surface

28. A couple of students at Putney decide to go bicycle riding one day Simon rides at a speed of 10 miles per hour, while Liz's average speed is 20 miles per hour After bicycling for several hours, both Simon and Liz come home and park their bicycles exactly where they started Simons's average velocity for the entire ride is

(A) lower than Liz's average velocity

(B) higher than Liz's average velocity

(C) zero

(D) impossible to determine without knowing the actual directions in which he biked

29. If, during their bike ride, Simon and Liz were always biking at a constant speed,

(A) their acceleration was always zero

(B) their velocity was constant

(C) their average velocity after one hour of biking was the same as their average velocity after two hours of biking

(D) None of the above

30. While sitting at his office desk, Stephen Greenblatt enjoys throwing crumpled pieces of paper into a wastebasket across the room Over the years, he has carefully kept track of all the different combinations of initial speeds and angles at which he can throw the crumpled pieces of paper while still making the same basket He hopes to some day have a complete list of all the possibilities Professor Greenblatt's efforts are useless because

(A) although such a list can theoretically be made, he will never have enough time to exhaust all possibilities

(B) there is really only one way to make the basket, and Greenblatt is confused about this because a janitor keeps moving the wastebasket at night

(C) there are infinitely many ways to make this basket from the same position

(D) None of the above