Assignment - Kinematics
Reading
Chapter 2
Objectives/HW
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The student will be able to: |
HW: |
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1 |
Define and distinguish the concepts scalar and vector. Make the connection between the visual representation of a vector and its numerical representation of magnitude and direction angle. |
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2 |
Define, distinguish, and apply the concepts: distance, displacement, position. |
1, 2 |
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3 |
Define, distinguish, and apply the concepts: average speed, instantaneous speed, constant speed, average velocity, instantaneous velocity, constant velocity. |
3 – 7 |
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4 |
Define, distinguish, and apply the concepts: average acceleration and instantaneous acceleration, and constant acceleration. |
8 – 14 |
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5 |
State the displacement and velocity relations for cases of constant acceleration and use these to solve problems given appropriate initial conditions and values. |
15 – 26 |
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6 |
State and use the conditions of freefall, including the value of g, to solve associated problems. |
27 – 36 |
Homework Problems
1. A NASA team oversees a space shuttle launch at Cape Canaveral and then travels to Edward's Air Force Base in California to supervise the landing. Which group of people, the astronauts or the NASA team has the greater displacement? the greater distance?
2. Assume the field in Neyland
Stadium runs perfectly north and south. Beginning with an initial position of
60.0 yds. , 90.0° from the south goal
post, Mr. M marches (in linear segments) the following four displacements in
succession: d1 = 10.0 yds, 0.0°,
d2 = 11.2 yds, 206.6°,
d3 = 11.2 yds, 333.4°,
d4 = 10.0 yds, 180.0°.
(a) Using a protractor and ruler measure out a diagram of Mr. M's
march. (b) From initial to final position what is the overall displacement?
(Hint: measure your diagram!) (c) From initial to final position what is the
total distance? (d) What is the final position?
3. The speed of light in
the vacuum of space or in air is a constant value of 3.00 x 108
m/s.
(a) A light-year is the distance traveled by light in one year. What is this
distance?
(b) What amount of time does it take for light to travel from the Moon to the
Earth – a distance of 384 Mm? (c) How much time would it take a car traveling
45 m/s (100 mph)?
4. An airport radar uses
the reflection (or "echo") of a radio signal to measure aircrafts'
positions. Suppose the position of a certain helicopter at 1:00 PM is 105 miles, 90.0° from the airport. At 1:30 PM it is 48 miles, 90.0° from the airport. (a) Find the
displacement of the helicopter over this interval of time. (b) Find the
average velocity of the helicopter.
(c) Assuming the velocity remains constant what is the position of the
helicopter at 1:45
PM?
Note: a diagram showing the airport and helicopter is very helpful!
5. You are driving down a street in a car at 55 km/h. Suddenly a child runs into the street. If it takes you 0.75 s to react and apply the brakes, how many meters will you travel before you begin to slow down?
6. You plan a trip on which you want to average 90 km/h. You travel the first half of the trip's distance at an average speed of only 50 km/h. What must your average speed be in the second half of the trip to meet your goal? (Is this a reasonable result?)
7. 
The graph below shows the motion of a
hummingbird. For the interval of time shown, determine the following: (a) What
is the bird’s greatest distance away from the flower?
(b) What is the bird’s most western position? (c) At what point(s) in time is
the bird at the flower? (d) Determine the bird’s average velocity. (e)
Determine the bird’s average speed. (f) What is the bird’s velocity at 10.0
s? (g) What is the bird’s velocity at 5.5 s? (h) At what position(s) is the
bird’s velocity equal to zero? (i) What is the bird’s maximum speed?
8. Again refer to the above graph. (a) The bird is moving with a constant velocity at what point(s) in time? (b) The bird is accelerating at what point(s) in time? (c) The bird’s speed is decreasing at what point(s) in time?
9. Answer the following and
explain or give an example: (a) Can an object have zero velocity and at the
same time be accelerating? (b) Can an object have a constant speed and a
changing velocity? (c) Can an object have a constant velocity and a changing
speed?
(d) Can an object be moving but not accelerating? (e) Can an object have
velocity and acceleration vectors that point in opposite directions?
10. A 1956 VW Van could go from 0 to 60 mph (26.8 m/s) in 75 seconds (as measured by Road & Track). (a) Determine the average rate of acceleration. (b) Assuming a braking deceleration of 9.0 m/s2 what amount of time was required to return from 60 mph to 0?
11. A supersonic jet that is flying at 200 m/s is accelerated uniformly at the rate of 23.1 m/s2 for 20.0 s. (a) What is its final speed? (b) The speed of sound in air is 331 m/s. How many times the speed of sound is the plane's final speed? (This is called the Mach number.)
12. Rocket-powered sleds are used to test the responses of humans to acceleration. Starting from rest, one sled can reach a speed of 444 m/s in 1.80 s and be brought to a stop again in the next 2.15 s. The rate of acceleration due to gravity is called a "g" and is equal to 9.80 m/s2. Determine the greatest rate of acceleration experienced by the rider and express your answer as some number of g's.
13. A proton is traveling with an initial velocity of 2.35 x 105 m/s, 180.0°. It is then accelerated uniformly 1.10 x 1012 m/s2, 0.0° in an electric field for a duration of 150 ns. Determine its final velocity after undergoing this acceleration.
14. 
The graph below shows the motion of an object.
For the interval of time shown, determine the following: (a) At what point(s)
in time is the object moving southward? (b) Find the maximum speed. (c) Find
the average acceleration from t = 16 s to t = 32 s. (d) Find the
acceleration at t = 4.0 s and state whether speed is increasing or
decreasing at that point.
(e) Find the acceleration at t = 26 s. (f) The acceleration is zero at
what point(s) in time?
(g) The speed of the object is decreasing at what point(s) in time?
15. A skateboarder starts from rest atop a slope that is 20.0 m long and accelerates uniformly 2.60 m/s per second down the slope. (a) What is the position of the skateboarder 3.00 s later? (b) What is the speed at that point? (c) How much time overall is needed to go down the slope?
16. The maximum deceleration rate of a typical car is about 10 m/s2.(a) Determine the distance required to stop your car when initially traveling 30 m/s. (b) Repeat for 60 m/s.
17. You are investigating an accident scene in which several cars wrecked in order to avoid a car skidding to a stop. The skid marks are 65 m long. A skidding car will have a deceleration rate of about 10 m/s2. How fast was this car going before it began to skid?
18. An object traveling on a horizontal surface with an initial velocity of 12.0 m/s to the right is then accelerated 3.00 m/s2 towards the left. (a) Calculate the magnitude of this object's displacement at values of time: 0.00, 4.00, and 8.00 s. (b) Calculate the speed for the same times. (c) Describe the motion of the object for this time interval.
19. At t = 0.00 s a ball is
started rolling up an inclined plane with an initial velocity of 6.00 m/s ,
15.0°. At t = 2.00 s the
ball reverses its direction and begins to roll back down. (a) How far up the
slope does the ball travel? (b) Find the ball's acceleration. (c) Find the
speed of the ball at t = 3.00 s. (d) Find the distance traveled by the ball
during these 3.00 seconds.
(e) Find the ball's position at t = 3.00 s.
20. (a) Determine the displacement of a plane traveling northward that is uniformly accelerated from 66 m/s to 88 m/s in 12 s. (b) Repeat the calculation for the same plane slowing down from 88 m/s to 66 m/s in 12 s and show that the result is the same.
21. The bullet leaves the muzzle of a certain rifle with a speed of 600 m/s. The barrel of the rifle is 90.0 cm long. Find the acceleration rate of the bullet.
22. A moving car decelerates for 5.0 s and comes to a complete stop. It travels 75 m in the process. (a) Determine its initial value of speed. (b) Determine its rate of deceleration.
23. When a certain traffic
light turns green, a waiting car starts off with constant acceleration of 3.0
m/s2. At the same instant a truck with constant speed 12 m/s passes
by the car in the next lane. (a) How far must the car travel in order to catch
up to the truck (and then pass)?
(b) How fast will the car be moving as it passes the truck?
24. Highway safety engineers design "soft" barriers so that cars hitting them will slow down at a safe rate. A person wearing a safety belt can withstand a deceleration rate of 300 m/s2. How thick should barriers be to safely stop a car that hits the barrier at 110 km/h and then slows to a stop as it crashes through and destroys the barrier?
25. A baseball pitcher throws a fastball at a speed of 44 m/s. The acceleration occurs as the pitcher holds the ball and moves it through a distance of about 3.5 m during the entire delivery motion. Calculate the acceleration rate, assuming it is uniform.
26. A driver of a car going
90.0 km/h suddenly sees the lights of a barrier 40.0 m ahead. It takes the
driver 0.75 s before he applies the brakes, and the deceleration rate during
braking is
10.0 m/s2. (a) Determine if the car hits the barrier. (b) Using
the same assumptions, what is the maximum speed at which the car could be
moving and not hit the barrier?
27. Under what circumstances is the effect of air resistance negligible on an object in freefall? i.e. When is the use of g = 9.80 m/s2 most valid?
28. One rock is dropped from a cliff, a second rock is thrown downward. When they reach the bottom, which rock has a greater speed? Which has a greater acceleration? Which reaches the ground in the least amount of time?
29. A stone is dropped into a very deep hole in the ground and it hits the bottom after falling for 2.80 s. (a) How deep is the hole? (b) What is the impact velocity of the stone?
30. Suppose a person drops
20.0 m (about 5 floors) from a burning building and onto an air bag. (a) What
will be the person's maximum speed during their fall?
(b) Repeat for a drop of 40.0 m.
31. A ball is thrown upward with an initial speed of 15.0 m/s. (a) Find the maximum height attained by the ball. (b) How much time does it take to reach the maximum height? How much time does it take to fall back down? (c) What is the ball's velocity when it reaches its initial position?
32. A punter goofs and punts
the football straight up. The hang time (total time in the air) is
4.00 s. (a) What height does the ball reach? (b) What initial velocity in
miles per hour does the ball have?
33. A kangaroo jumps to a vertical height of 2.8 m. What is its total time in the air?
34. A juggler throws a beanbag straight up into the air with initial speed 6.00 m/s. The beanbag leaves the juggler's hand 1.50 m above the floor. The juggler fails to catch the beanbag as it falls to the floor. (a) How long is the beanbag in the air? (b) What is its impact speed?
35. As a part of a movie stunt a stunt man hangs from the bottom of an elevator that is rising at a steady rate of 1.10 m/s. The man lets go of the elevator and drops in freefall for 1.50 s before being caught by a rope that is attached to the bottom of the elevator. (a) Calculate the speed of the man at the instant he is caught by the rope. (b) How long is the rope? (c) How much closer to the ground is the man at the instant he is caught by the rope than he was at the instant he let go of the elevator?
36. A tennis ball is dropped from 1.20 m above the ground. It rebounds to a height of 1.00 m. (a) With what velocity does it hit the ground? (b) With what velocity does it leave the ground? (c) If the ball were in contact with the ground for 0.010 s find its acceleration while touching the ground. (i.e. the acceleration of the "bounce")