Chapter 12 Math Practice

Speed = distance/time 365 days = 1 year

Velocity =distance/time + direction 0.62 miles = 1 km

Acceleration = change in velocity/time

Momentum =mass x velocity

Distance =
½ X acceleration x time^{2 } 100 cm = 1m

Acceleration Due to Gravity = 9.8 m/sec^{2} or 32
ft/ sec^{2}

weight = Force = mass x acceleration N/kg = m/sec/sec

Universal Law of Gravitation Force_{gravity} = Gravitational constant(mass_{1}mass_{2})/radius^{2}

Gravitational constant = 6.67 x 10^{-11} N-m^{2}/kg^{2}

kg-m/sec/sec = N velocity of sound = 1100 ft/sec

On a separate sheet of paper

FOR EACH PROBLEM DO THE FOLLOWING ALWAYS!!!!!

A. Write the formula that you intend to use to solve the problem. 1 pt.

B. Show everything you did to get to the answer. 2 pts.

C. Circle your final answer. 1 pt.

- A jogger runs the first 1000m of a race in 250 sec. What is the jogger’s speed?

2. A student practicing for a track meet ran 250 m in 30 sec. What was her average velocity?

- A Space Shuttle travels in orbit at 21,000 km/hr. How far will the Space Shuttle travel after 5 hours?

- A car traveled 1025 km from El Paso to Dallas in 13.5 hours. What was its average velocity?

- How fast was a plane flying if it traveled 400 km in 30 min?

- If the average speed of a car is 45 km/hr, how far can the car travel in 40 min?

- The
speed of light is 3 x 10
^{8}m/sec. How long does it take light to travel

149 x 10^{9} m distance from the sun to the earth?

- If the speedometer of your car reads 30 mph, how far will you go in 15 min?

- The table below shows Jack’s travels on his skateboard.

Time (sec) |
Distance (m) |

0 |
0 |

5 |
30 |

10 |
70 |

15 |
90 |

20 |
120 |

A. What was Jack’s speed from T5 to T 10 seconds?

B. What was Jack’s average speed for the entire ride?

- A car accelerates from 0 to 72km/hr in 8 sec. What is the car’s acceleration?

- A space ship is traveling at 20,000 m/sec. At T=5 sec, the rocket thrusters are turned on. At T =55 sec, the space ship reaches a speed of 24,000 m/sec. What is the space ship’s acceleration?

- A driver starts his parked car and within 5 sec reaches a velocity of 54 km/hr as he travels east. What is his acceleration?

- A car-traveling north with a velocity of 30 m/sec slows down to a velocity of 10 m/sec within 10 sec. What is the cars deceleration?

- A sprinter accelerates out of the starting blocks to a speed of 10 m/sec in one sec. What is the sprinters acceleration?

- If a car completes a 3-mile oval track in 58 seconds, what is the average speed? Explain whether or not the car accelerated during this 58 seconds.

- If your car goes from 0 to 60 miles per hour in 6 seconds, what is the average acceleration?

- Falling objects travel at an average acceleration of 9.8 m/sec/sec. If an object falls from a tall building, how long will it take before it reaches a speed of 49 m/sec?

- A
penny is dropped from the top of the Sears Tower in Chicago. Acceleration due to gravity is 32
ft/sec
^{2}. It takes 9.5 seconds to fall. What is the velocity of the penny just before hitting the ground?

- A student drops a rock down a mineshaft. It takes 3 seconds for the rock to hit the bottom of the shaft, what is the velocity of the rock just before impact? The acceleration due to gravity is 9.8 m/sec/sec.

- The hare and the tortoise are at the starting line together. When the gun goes off, the hare moves off at a constant speed of 10 meters per second. The tortoise starts more slowly, but accelerates at the rate of 1 meter per second per second. Make a table showing the positions of the two racers after 1 second, 2 second, 3 seconds, and so forth until the tortoise passes the hare.

- A stone is dropped from a bridge and hits the water 2.5 s later. What is the final velocity of the stone? What is the height of the bridge?

- A parachutist jumps from a plane and starts to freefall at 1500 ft. His parachute fails to deploy. Make a table and a graph of his velocity and distance every 250 ft.

- A rock falls to the bottom of a tall canyon, falling freely with no air resistance, for 4.5 seconds. Make a table of the distance traveled by the rock and its velocity after 1.0 s, 2.0 s, 3.0 s, 3.5 s and 4.5 s.

- A steel ball whose mass is 100 g is rolling at a rate of 2.8 m/sec. What is its momentum?

- A marble is rolling at a velocity of 100 cm/sec with a momentum of 10,000g-cm/sec. What is its mass?

- An object whose mass is 3 kg is fired from a cannon, giving it forward momentum of 1050kg-m/sec. What is its velocity?

- What is the momentum of a 200-g rifle bullet traveling at 300 m/sec?

- What is the momentum of a 1000 kg truck that is traveling at 0.1 m/sec?

- A race walker can walk 1 mile in 10 minutes. What is the speed in miles per hour? In km per hour?

- How long will it take the above race walker to walk 3 miles? 10 km?

- How far can the above race walker walk in 45 minutes? In 1.5 hours?

- The North American Plate is moving away from the European plate at a constant speed of 4.2 cm per year?
- If the average distance between the two plates is 7000 km, and the two plates have maintained their constant speeds, how long ago were the two plates together?

- A typical motorist in the United States travels 25,000 miles in his or her car every year. If you assume that the average speed of the car while traveling is 45 miles per hour, calculate the total number of hours an average motorist spends in his or her car. How many hours per day?

- The typical airborne speed of an intercontinental 747 jet is 530 miles per hour, while the airborne speed of the supersonic Concorde is 1500 miles per hour. If each airliner were to circumnavigate the earth (25,000miles) what would be the difference in air time between the two aircraft?

- It
takes light 8.33 minutes to travel from the sun to earth, and 1.3 seconds
from earth to the moon. What is
the average distance of the sun and moon from earth? The speed of light is 3 x 10
^{8}m/s.

- While traveling out in the country at 50 miles per hour, your car’s engine and brakes stop working and you coast to a stop in 25 seconds. What was your average deceleration during the time after the motor stopped working until you stopped?

- Starting from rest, a train will reach a final, constant speed in 35 seconds while accelerating at a constant speed of 3 km/hr/sec. What is the final speed of the train?

- 50 N of force is applied to move a round rock that has a mass of 5.0 kg. What will be the acceleration of the rock when the force is applied?

- A 2.5
kg bowling ball accelerated at a rate of 50 m/sec
^{2}. What was the force that was applied to the bowling ball?

- What is the force on a 10 kg ball that is freefalling due to the pull of gravity?

- A man has a mass of 66 kg on earth. What is his weight?

- A girl on roller skates accelerates at a rate of 2 m/sec/sec with a force of 100 N. What is her mass?

- A person weighs 540 N on the earth. What is the person’s mass?

- On the moon the acceleration due to gravity is 1.67 N/kg. What is the weight of a person on the moon with a mass of 60 kg?

- What is the gravitational attraction between an 80 kg man and a 50 kg woman who are 2 m apart?

- What
is the distance between two 3200 kg elephants when they are apart and
exerting a gravitational force of 3.8 x 10
^{4}N?

- The
acceleration due to gravity on the surface of Mars is 0.4 m/s
^{2}. How much would a man weigh on the surface of Mars if his weight on earth is 180 N?

- Jupiter
has a mass of 1.9 x 10
^{27}kg. The sun has a mass of 2 x 10^{30}kg. The distance between Jupiter and the sun is 7.8 x 10^{8}km. What is the gravitational force between the sun and Jupiter?

- Earth
has a mass of 6.0 x 10
^{24}kg. The distance from the sun to the earth is 1.5 x 10^{11}m. The gravitational force between the sun and earth is 3.6 x 10^{22}N. What is the mass of the sun?

- Where is it easier for a person to swim, on the earth or on the moon? Assume that they both have liquid water.

- Are the gravitational forces on two identical masses- one of them floating in water and one lying on a table identical? Explain why.

- A rocket leaves earth along a radial path with a constant acceleration equal to the acceleration due to gravity at the earth’s surface. How does the weight of a passenger change with distance from the earth?

- Will the air density in a spacecraft change when it enters the state of weightlessness? Explain why.

- Why does an object weigh less at the equator than at the poles?

- A 90 kg man stands in an elevator cab. When it starts to move the scale reads 720 N. Is the cab moving upward or downward? Explain. Is its velocity constant? What is its acceleration?

- A hole is drilled to the center of the earth and a 1 kg stone is dropped into the hole. What is the mass of the stone when it hits the bottom of the hole? Explain.

- The moon’s mass is approximately 1% of the earth’s mass. How does the gravitational pull of the moon on the earth compare with the gravitational pull of the earth on the moon?

- A 55 N woman stands on a scale in an elevator. What does the scale read when the elevator is ascending at a constant velocity of 12 m/s? What does the scale read when the elevator is ascending at a constant acceleration of 3 m/s/s? What does the scale read when the elevator is in freefall because the cable broke?

- Are there any circumstances when an object can be moving in a curved path and not be accelerating? Explain.