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physics
college physics 2nd
College Physics 2nd Edition OpenStax - Solutions
A student drove to the university from their home and noted that the odometer reading of their car increased by 12.0 km. The trip took 18.0 min. (a) What was their average speed?(b) If the straight- line distance from their home to the university is 10.3 km in a direction 25.0º south of east,
On dry concrete, a car can decelerate at a rate of 7.00m/s2 , whereas on wet concrete it can decelerate at only 7.00m/s2. Find the distances necessary to stop a car moving at 30.0 m/s (about 110 km/h)(a) On dry concrete and(b) On wet concrete.(c) Repeat both calculations, finding the displacement
How are instantaneous velocity and instantaneous speed related to one another? How do they differ?
The speed of propagation of the action potential (an electrical signal) in a nerve cell depends (inversely) on the diameter of the axon (nerve fiber). If the nerve cell connecting the spinal cord to your feet is 1.1 m long, and the nerve impulse speed is 18 m/s, how long does it take for the nerve
Is it possible for speed to be constant while acceleration is not zero? Give an example of such a situation.
Conversations with astronauts on the lunar surface were characterized by a kind of echo in which the earthbound person’s voice was so loud in the astronaut’s space helmet that it was picked up by the astronaut’s microphone and transmitted back to Earth. It is reasonable to assume that the
Give an example in which velocity is zero yet acceleration is not.
Is it possible for velocity to be constant while acceleration is not zero? Explain.
The acceleration due to gravity on Earth differs slightly from place to place, depending on topography (e.g., whether you are on a hill or in a valley) and subsurface geology (whether there is dense rock like iron ore as opposed to light rock like salt beneath you.) The precise acceleration due to
What happens if the person on the cliff throws the rock straight down, instead of straight up? To explore this question, calculate the velocity of the rock when it is 5.10 m below the starting point, and has been thrown downward with an initial speed of 13.0 m/s.StrategyDraw a sketch.Since up is
If a subway train is moving to the left (has a negative velocity) and then comes to a stop, what is the direction of its acceleration? Is the acceleration positive or negative?
A cheetah can accelerate from rest to a speed of 30.0 m/s in 7.00 s. What is its acceleration?
Find the average velocity of the car whose position is graphed in Figure 2.45.Data given in Figure 2.45StrategyThe slope of a graph of x vs. t is average velocity, since slope equals rise over run. In this case, rise = change in position and run = change in time, so thatSince the slope is constant
Professional Application Dr. John Paul Stapp was U.S. Air Force officer who studied the effects of extreme deceleration on the human body. On December 10, 1954, Stapp rode a rocket sled, accelerating from rest to a top speed of 282 m/s (1015 km/h) in 5.00 s, and was brought jarringly back to rest
Plus and minus signs are used in one-dimensional motion to indicate direction. What is the sign of an acceleration that reduces the magnitude of a negative velocity? Of a positive velocity?
What information do you need in order to choose which equation or equations to use to solve a problem? Explain.
Calculate the acceleration of the jet car at a time of 25 s by finding the slope of the vs. graph in Figure 2.49(a).Data given in Figure 2.49StrategyThe slope of the curve at t=25 s is equal to the slope of the line tangent at that point, as illustrated in Figure 2.49(a). Velocity, v
A commuter backs her car out of her garage with an acceleration of 1.40 m/s2.(a) How long does it take her to reach a speed of 2.00 m/s?(b) If she then brakes to a stop in 0.800 s, what is her deceleration?
What is the last thing you should do when solving a problem? Explain.
Assume that an intercontinental ballistic missile goes from rest to a suborbital speed of 6.50 km/s in 60.0 s (the actual speed and time are classified). What is its average acceleration in m/s2 and in multiples of g (9.80 m/s2)?
What is the acceleration of a rock thrown straight upward on the way up? At the top of its flight? On the way down?
An Olympic-class sprinter starts a race with an acceleration of 4.50 m/s. (a) What is her speed 2.40 s later?(b) Sketch a graph of her position vs. time for this period.
An object that is thrown straight up falls back to Earth. This is one-dimensional motion. (a) When is its velocity zero?(b) Does its velocity change direction?(c) Does the acceleration due to gravity have the same sign on the way up as on the way down?
Suppose you throw a rock nearly straight up at a coconut in a palm tree, and the rock misses on the way up but hits the coconut on the way down. Neglecting air resistance, how does the speed of the rock when it hits the coconut on the way down compare with what it would have been if it had hit the
A bullet in a gun is accelerated from the firing chamber to the end of the barrel at an average rate of 6.20 x 105 m/s2 for 8.10 x 10-4s. What is its muzzle velocity (that is, its final velocity)?
If an object is thrown straight up and air resistance is negligible, then its speed when it returns to the starting point is the same as when it was released. If air resistance were not negligible, how would its speed upon return compare with its initial speed? How would the maximum height to which
(a) A light-rail commuter train accelerates at a rate of 1.35 m/s2. How long does it take to reach its top speed of 80.0 km/h, starting from rest?(b) The same train ordinarily decelerates at a rate of 1.65 m/s2. How long does it take to come to a stop from its top speed? (c) In emergencies the
The severity of a fall depends on your speed when you strike the ground. All factors but the acceleration due to gravity being the same, how many times higher could a safe fall on the Moon be than on Earth (gravitational acceleration on the Moon is about 1/6 that of the Earth)?
(a) Explain how you can use the graph of position versus time in Figure 2.52 to describe the change in velocity over time. Identify (b) The time (ta, tb, tc, td, or te) at which the instantaneous velocity is greatest,(c) The time at which it is zero, and(d) The time at which it is negative.
While entering a freeway, a car accelerates from rest at a rate of 2.40 m/s2 for 12.0 s. (a) Draw a sketch of the situation.(b) List the knowns in this problem.(c) How far does the car travel in those 12.0 s? To solve this part, first identify the unknown, and then discuss how you chose the
How many times higher could an astronaut jump on the Moon than on Earth if his takeoff speed is the same in both locations (gravitational acceleration on the Moon is about 1/6 of on Earth)?
At the end of a race, a runner decelerates from a velocity of 9.00 m/s at a rate of 2.00 m/s2. (a) How far does she travel in the next 5.00 s? (b) What is her final velocity?(c) Evaluate the result. Does it make sense?
(a) Sketch a graph of velocity versus time corresponding to the graph of position versus time given in Figure 2.53. (b) Identify the time or times (ta, tb, tc, etc.) at which the instantaneous velocity is greatest.(c) At which times is it zero?(d) At which times is it negative? Position
(a) Explain how you can determine the acceleration over time from a velocity versus time graph such as the one in Figure 2.54.(b) Based on the graph, how does acceleration change over time? a Velocity 22 V1 P t1 Time t 1 I I I 1 I I I 1 I I ħ2
In a slap shot, a hockey player accelerates the puck from a velocity of 8.00 m/s to 40.0 m/s in the same direction. If this shot takes 3.33 x 10-2 s, calculate the distance over which the puck accelerates.
(a) Sketch a graph of acceleration versus time corresponding to the graph of velocity versus time given in Figure 2.55.(b) Identify the time or times (ta, tb, tc, etc.) at which the acceleration is greatest.(c) At which times is it zero?(d) At which times is it negative? Velocity a b d f 8 Time
A powerful motorcycle can accelerate from rest to 26.8 m/s (100 km/h) in only 3.90 s. (a) What is its average acceleration? (b) How far does it travel in that time?
Consider the velocity vs. time graph of a person in an elevator shown in Figure 2.56. Suppose the elevator is initially at rest. It then accelerates for 3 seconds, maintains that velocity for 15 seconds, then decelerates for 5 seconds until it stops. The acceleration for the entire trip is not
Freight trains can produce only relatively small accelerations and decelerations. (a) What is the final velocity of a freight train that accelerates at a rate of 0.0500 m/s2 for 8.00 min, starting with an initial velocity of 4.00 m/s?(b) If the train can slow down at a rate of 0.550 m/s2, how long
A fireworks shell is accelerated from rest to a velocity of 65.0 m/s over a distance of 0.250 m.(a) How long did the acceleration last?(b) Calculate the acceleration.
A swan on a lake gets airborne by flapping its wings and running on top of the water. (a) If the swan must reach a velocity of 6.00 m/s to take off and it accelerates from rest at an average rate of 0.350 m/s2, how far will it travel before becoming airborne?(b) How long does this take?
An unwary football player collides with a padded goalpost while running at a velocity of 7.50 m/s and comes to a full stop after compressing the padding and his body 0.350 m. (a) What is his deceleration? (b) How long does the collision last?
A cylinder is given a push and then rolls up an inclined plane. If the origin is the starting point, sketch the position, velocity, and acceleration of the cylinder vs. time as it goes up and then down the plane.
In World War II, there were several reported cases of airmen who jumped from their flaming airplanes with no parachute to escape certain death. Some fell about 20,000 feet (6000 m), and some of them survived, with few life-threatening injuries. For these lucky pilots, the tree branches and snow
Consider a grey squirrel falling out of a tree to the ground.(a) If we ignore air resistance in this case (only for the sake of this problem), determine a squirrel’s velocity just before hitting the ground, assuming it fell from a height of 3.0 m.(b) If the squirrel stops in a distance of 2.0 cm
An express train passes through a station. It enters with an initial velocity of 22.0 m/s and decelerates at a rate of 0.150 m/s2 as it goes through. The station is 210 m long.(a) How long did the nose of the train stay in the station?(b) How fast is it going when the nose leaves the station?(c) If
A bicycle racer sprints at the end of a race to clinch a victory. The racer has an initial velocity of 11.5 m/s and accelerates at the rate of 0.500 m/s2 for 7.00 s.(a) What is his final velocity?(b) The racer continues at this velocity to the finish line. If he was 300 m from the finish line when
In 1967, New Zealander Burt Munro set the world record for an Indian motorcycle, on the Bonneville Salt Flats in Utah, with a maximum speed of 183.58 mi/h. The one-way course was 5.00 mi long. Acceleration rates are often described by the time it takes to reach 60.0 mi/h from rest. If this time was
(a) A world record was set for the men’s 100-m dash in the 2008 Olympic Games in Beijing by Usain Bolt of Jamaica. Bolt “coasted” across the finish line with a time of 9.69 s. If we assume that Bolt accelerated for 3.00 s to reach his maximum speed, and maintained that speed for the rest of
Calculate the displacement and velocity at times of (a) 0.500, (b) 1.00,(c) 1.50,(d) 2.00, and(e) 2.50 s for a rock thrown straight down with an initial velocity of 14.0 m/s from the Verrazano Narrows Bridge in New York City. The roadway of this bridge is 70.0 m above the water.
A basketball referee tosses the ball straight up for the starting tip-off. At what velocity must a basketball player leave the ground to rise 1.25 m above the floor in an attempt to get the ball?
A rescue helicopter is hovering over a person whose boat has sunk. One of the rescuers throws a life preserver straight down to the victim with an initial velocity of 1.40m/s and observes that it takes 1.8 s to reach the water.(a) List the knowns in this problem.(b) How high above the water was the
Certain criteria must be satisfied if a measurement or observation is to be believed. Will the criteria necessarily be as strict for an expected result as for an unexpected result?
Soccer fields vary in size. A large soccer field is 115 m long and 85 m wide. What are its dimensions in feet and inches?
Perform the following calculations and express your answer using the correct number of significant digits.(a) A woman has two bags weighing 13.5 pounds and one bag with a weight of 10.2 pounds. What is the total weight of the bags?(b) The force on an object is equal to its mass multiplied by its
Can the validity of a model be limited, or must it be universally valid? How does this compare to the required validity of a theory or a law?
What is the height in meters of a person who is 6 ft 1.0 in. tall?
Using mental math and your understanding of fundamental units, approximate the area of a regulation basketball court. Describe the process you used to arrive at your final approximation.
Classical physics is a good approximation to modern physics under certain circumstances. What are they?
Mount Everest, at 29,028 feet, is the tallest mountain on the Earth. What is its height in kilometers?
When is it necessary to use relativistic quantum mechanics?
The speed of sound is measured to be 342m/s on a certain day. What is this in km/h?
Can classical physics be used to accurately describe a satellite moving at a speed of 7500 m/s? Explain why or why not.
Tectonic plates are large segments of the Earth’s crust that move slowly. Suppose that one such plate has an average speed of 4.0 cm/year. (a) What distance does it move in 1 s at this speed?(b) What is its speed in kilometers per million years?
Identify some advantages of metric units.
What is the relationship between the accuracy and uncertainty of a measurement?
Suppose that your bathroom scale reads your mass as 65 kg with a 3% uncertainty. What is the uncertainty in your mass (in kilograms)?
Prescriptions for vision correction are given in units called diopters (D). Determine the meaning of that unit. Obtain information (perhaps by calling an optometrist or performing an internet search) on the minimum uncertainty with which corrections in diopters are determined and the accuracy with
A good-quality measuring tape can be off by 0.50 cm over a distance of 20 m. What is its percent uncertainty?
(a) A car speedometer has a 5.0% uncertainty. What is the range of possible speeds when it reads 90 km/h?(b) Convert this range to miles per hour. (1 km 0.6214 mi)
An infant's pulse rate is measured to be 130 ±5 beats/min. What is the percent uncertainty in this measurement?
(a) Suppose that a person has an average heart rate of 72.0 beats/min. How many beats do they have in 2.0 y? (b) In 2.00 y?(c) In 2.000 y?
A can contains 375 mL of soda. How much is left after 308 mL is removed?
State how many significant figures are proper in the results of the following calculations: (a) (106.7)(98.2)/(46.210)(1.01) (b) (18.7)2(c) (1.60 x 10-19) (3712).
(a) How many significant figures are in the numbers 99 and 100? (b) If the uncertainty in each number is 1, what is the percent uncertainty in each?(c) Which is a more meaningful way to express the accuracy of these two numbers, significant figures or percent uncertainties?
(a) If your speedometer has an uncertainty of 2.0 km/h at a speed of 90 km/h, what is the percent uncertainty? (b) If it has the same percent uncertainty when it reads 60 km/h, what is the range of speeds you could be going?
(a) A person's blood pressure is measured to be 120 ± 2 mm Hg. What is its percent uncertainty?(b) Assuming the same percent uncertainty, what is the uncertainty in a blood pressure measurement of 80 mm Hg?
A person measures their heart rate by counting the number of beats in 30 s. If 40 ± 1 beats are counted in 30.0 ± 0.5 s, what is the heart rate and its uncertainty in beats per minute?
What is the area of a circle in diameter?
If a marathon runner averages 9.5 mi/h, how long does it take him or her to run a 26.22-mi marathon?
A marathon runner completes a 42.188-km course in 2 h, 30 min, and 12 s. There is an uncertainty of 25 m in the distance traveled and an uncertainty of 1 s in the elapsed time.(a) Calculate the percent uncertainty in the distance.(b) Calculate the uncertainty in the elapsed time.(c) What is the
The sides of a small rectangular box are measured to be 1.80 ± 0.01 cm, 2.05 ± 0.02 cm, and 3.1 ± 0.1 cm long. Calculate its volume and uncertainty in cubic centimeters.
A generation is about one-third of a lifetime. Approximately how many generations have passed since the year 0 AD?
How many times longer than the mean life of an extremely unstable atomic nucleus is the lifetime of a human?
Calculate the approximate number of atoms in a bacterium. Assume that the average mass of an atom in the bacterium is ten times the mass of a hydrogen atom.
Approximately how many atoms thick is a cell membrane, assuming all atoms there average about twice the size of a hydrogen atom?
(a) What fraction of Earth’s diameter is the greatest ocean depth? (b) The greatest mountain height?
(a) Calculate the number of cells in a hummingbird assuming the mass of an average cell is ten times the mass of a bacterium. (b) Making the same assumption, how many cells are there in a human?
Assuming one nerve impulse must end before another can begin, what is the maximum firing rate of a nerve in impulses per second?
Give an example in which there are clear distinctions among distance traveled, displacement, and magnitude of displacement. Specifically identify each quantity in your example.
A racehorse coming out of the gate accelerates from rest to a velocity of 15.0 m/s due west in 1.80 s. What is its average acceleration?StrategyFirst we draw a sketch and assign a coordinate system to the problem. This is a simple problem, but it always helps to visualize it. Notice that we assign
A cyclist rides 3 km west and then turns around and rides 2 km east. (a) What is their displacement?(b) What distance do they ride?(c) What is the magnitude of their displacement?
How many heartbeats are there in a lifetime?
A car engine moves a piston with a circular cross section of 7.500 ± 0.002 cm diameter a distance of 3.250 ± 0.001 cm to compress the gas in the cylinder. (a) By what amount is the gas decreased in volume in cubic centimeters?(b) Find the uncertainty in this volume.
When non-metric units were used in the United Kingdom, a unit of mass called the pound-mass (lbm) was employed, where 1 lbm = 0.4539 kg. (a) If there is an uncertainty of 0.0001 kg in the pound-mass unit, what is its percent uncertainty? (b) Based on that percent uncertainty, what mass in
The glue on a piece of tape can exert forces. Can these forces be a type of simple friction? Explain, considering especially that tape can stick to vertical walls and even to ceilings.
Find the terminal velocity of an 85-kg skydiver falling in a spread-eagle position.StrategyAt terminal velocity, Fnet = 0. Thus the drag force on the skydiver must equal the force of gravity (the person’s weight). Using the equation of drag force, we findThus the terminal velocity vt can be
(a) When rebuilding her car’s engine, a physics major must exert 300 N of force to insert a dry steel piston into a steel cylinder. What is the magnitude of the normal force between the piston and cylinder?(b) What is the magnitude of the force would she have to exert if the steel parts were
Suspension cables are used to carry gondolas at ski resorts. (See Figure 5.14) Consider a suspension cable that includes an unsupported span of 3020 m. Calculate the amount of stretch in the steel cable. Assume that the cable has a diameter of 5.6 cm and the maximum tension it can withstand is 3.0
When you learn to drive, you discover that you need to let up slightly on the brake pedal as you come to a stop or the car will stop with a jerk. Explain this in terms of the relationship between static and kinetic friction.
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