Physics final, problems

Suppose that a binary-star system consists of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?

4.3X10 29 kg

A hypothetical planet has a radius 1.5 times that of Earth, but has the same mass. What is the acceleration due to gravity near its surface?

4.4 m/s2

At room temperature, an oxygen molecule, with mass of 5.31×10−26 typically has a KE of about 6.12×10−21 J. How fast is the molecule moving?

484 m/s

At what minimum speed must a roller coaster be traveling when upside down at the top of a circle so that the passengers will not fall out? Assume a radius of curvature of 7.4 m.

8.5 m/s

A 65-kg trampoline artist jumps vertically upward from the top of a platform with a speed of 5.0 𝑚 𝑠⁄ . (a) How fast is he going as he lands on the trampoline, 3.0 m below? (b) If the trampoline behaves like a spring with spring stiffness constant 6.2×104 𝑁 𝑚⁄ , how far does he depress it?

9.2 m/s (b) 0.31m

A 55-kg hiker starts at an elevation of 1600 m and climbs to the top of a 3300-m peak. (a) What is the hiker's change in potential energy? (b) What is the minimum work required of the hiker? (c) Can the actual work done be more than this? Explain why.

9.2X105 J, 9.2x105 J, yes

A ladder, leaning against a wall, makes a 60º angle with the ground. When is it more likely to slip: when a person stands on the ladder near the top or near the bottom? Explain.

A ladder is more likely to slip when a person is near the top than when he is near the bottom.

(a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kilohertz) and travel with a speed of .sm 1000.3 8 What are the wavelengths of these signals? (b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?

AM 190m to 550 m, FM 2.78 m to 3.41 m

If you dangle two pieces of paper vertically, a few inches apart, and blow between them, how do you think the papers will move? Try it and see. Explain.

Air when blown between the two dangling vertical sheets of paper, they will move forward to each other. This is because, when the air that is blown between them will lower the pressure. As the pressure outside is higher when compared between the two sheets, they move close to each other

Suppose you are sitting on a rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Before you drop the masses the total rotational inertia of the system (you, the stool, and the masses) is your moment of inertia plus the moment of inertia of the stool plus the moment of inertia of the masses. But dropping the masses doesn't change their moment of inertia so your moment of inertia doesn't change unless you change the position of your body. Since your moment of inertia doesn't change your angular velocity doesn't change.Another way to think about this is in terms of angular momentum. At the instant you drop the masses they are moving tangent to the circle and so they have the same angular momentum they had just before you dropped them. So you have the same angular momentum after dropping them as before and therefore the same angular velocity.Finally we can think about his in terms of work and energy. You do no work on the masses when you drop them (since you just let go of them, you don't move them through a distance) so your rotational kinetic energy doesn't change and your angular velocity doesn't change.

Calculate the speed of a satellite moving in a stable circular orbit about the Earth at a height of 3600 km.

Calculate the speed of a satellite moving in a stable circular orbit about the Earth at a height of 3600 km.

A bucket of water can be whirled in a vertical circle without the water spilling out, even at the top of the circle when the bucket is upside down. Explain.

Centrifugal force is at work. This force is pushing the water away from the center.

If the speed of a particle triples, by what factor does its kinetic energy increase?

For a threefold increase in speed, the kinetic energy will increase by a factor of nine.

Suppose a disk rotates at constant angular velocity. Does a point on the rim have rdial and/or tangential acceleration? If the disk's angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

If a disk rotates at constant angular velocity, a point on the rim has radial acceleration only - no tangential acceleration. If the disk's angular velocity increases uniformly, the point will have both radial and tangential acceleration.

If there were a great migration of people toward the Earth's equator, how would this affect the length of the day?

If mass moves to the equator, it is further from the axis of rotation, so the rotational inertia of the earth increases. Because the angular momentum of the earth is conserved, this means its rotational speed decreases, i.e. the length of the day would be longer.

Can an object be increasing in speed as its acceleration decreases? If so, give an example. If not, explain.

If the car is going in the negative direction

What would your bathroom scale read if you weighed yourself on an inclined plane? Assume the mechanism functions properly, even at an angle.

the bathroom scale would read the magnitude of the normal force between you and the plane, which would be Wcostheta

If the net force on a system is zero, is the net torque also zero? If the net torque on a system is zero, is the net force zero?

the object would not translate but there is a net torque. So it would rotate. If the net torque on a system is zero, is the net force also zero? No, forces add so the net force is not zero but the net torque is zero.

Why don't ships made of iron sink?

the ship is hollow and the empty space contains air which makes the average density of the ship less than that of water and hence it floats on water.

A stone hangs by a fine thread from the ceiling, and a section of the same thread dangles from the bottom of the stone. If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

the tension in the upper string will be larger than the tension in the lower string because of the weight of the stone. So, the upper string will break first.

Suppose you lift a suitcase from the floor to a table. The work you do on the suitcase depends on which of the following: (a) whether you lift it straight up or along a more complicated path, (b) the time it takes, (c) the height of the table, and (d) the weight of the suitcase?

when you lift a suitcase from the floor and keep it on a table then the work done by you on the suitcase depends on the weight of the suitcase.

Will an object weigh more at the equator or at the poles? What two effects are at work? Do they oppose each other?

you weigh less on the equator than at the North or South Pole

A cooling fan is turned off when it is running at 850 rev min.⁄ It turns 1500 revolutions before it comes to a stop. (a) What was the fan's angular acceleration, assumed constant? (b) How long did it take the fan to come to a complete stop?

(a) -0.42 rad/s2 (b) 210 sec

A force of 48.0 N is required to start a 5.0-kg box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor? (b) If the 48.0-N force continues, the box accelerates at .sm 70.0 2 What is the coefficient of kinetic friction?

(a) 0.98 (b) 0.91

A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is 25.0 N. (a) Find the speed of the bucket. (b) How fast must the bucket move at the top of the circle so that the rope does not go slack?

(a) 1.7 m/s (b) 3.28 m/s

A pendulum makes 36 vibrations in exactly 60 s. What is its (a) period, and (b) frequency? ?

(a) 1.7 s (b) 0.60 Hz

A 28.0-kg block is connected to an empty 1.35-kg bucket by a cord running over a frictionless pulley. The coefficient of static friction between the table and the block is 0.450 and the coefficient of kinetic friction between the table and the block is 0.320. Sand is gradually added to the bucket until the system just begins to move. (a) Calculate the mass of sand added to the bucket. (b) Calculate the acceleration of the system

(a) 11.3 kg (b) 0.88 m/s2

a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate its angular velocity in .srad (b) What are the linear speed and acceleration of a point on the edge of the grinding wheel?

(a) 260 rad/sec (b) 46 m/s, 12,000 m/s2

A box weighing 77.0 N rests on a table. A rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs (a) 30.0 N, (b) 60.0 N, and (c) 90.0 N.

(a) 47.0 N (b) 17.0 N (c) 0N

A 50-dB sound wave strikes an eardrum whose area is .m 100.5 25− (a) How much energy is absorbed by the eardrum per second? (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?

(a) 5.0X10-12 W (b) 6300 years

A projectile is fired with an initial speed of 65.2 m/s at an angle of 34.5º above the horizontal on a long flat firing range. Determine (a) the maximum height reached by the projectile, (b) the total time in the air, (c) the total horizontal distance covered (that is, the range), and (d) the velocity of the projectile 1.50 s after firing

(a) 69.6 m (b) 7.45 sec (c) 405 m (d) 58.1 m/s at 22.50 above horizontal

A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and rolls without slipping down a 30.0º incline that is 10.0 m long. (a) Calculate its translational and rotational speeds when it reaches the bottom. (b) What is the ratio of translational to rotational KE at the bottom? Avoid putting in numbers until the end so you can answer: (c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

(a) 8.37 m/s, 41.8 rad/s (b) 2.5

A person pushes a 14.0-kg lawn mower at constant speed with a force of N 0.88=F directed along the handle, which is at an angle of 45.0º to the horizontal. (a) Draw the free-body diagram showing all forces acting on the mower. Calculate (b) the horizontal friction force on the mower, then (c) the normal force exerted vertically upward on the mower by the ground. (d) What force must the person exert on the lawn mower to accelerate it from rest to sm 5.1 in 2.5 seconds, assuming the same friction force?

(b) 62.2 N (c) 199N (d) 99.9 N

The blades in a blender rotate at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow down?

- 2.3x102 rad/s2

A person stands on a bathroom scale in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person's regular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.

- 2.5 m/s2

A car slows down from sm 23 to rest in a distance of 85 m. What was its acceleration, if assumed constant?

-3.1 m/s2

A 6.0-cm-diameter pipe gradually narrows to 4.0 cm. When water flows through this pipe at a certain rate, the gauge pressure in these two sections is 32.0 kPa and 24.0 kPa, respectively. What is the volume rate of flow?

0.0056 m3/s

In a "Rotor-ride" at a carnival, people are rotated in a cylindrically walled "room." The room radius is 4.6 m, and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]

0.22

What is the magnitude of the momentum of a 28-g sparrow flying with a speed of 8.4 𝑚 𝑠⁄ ?

0.24 kg m/s

A sports car moving at constant speed travels 110 m in 5.0 s. If it then brakes and comes to a stop in 4.0 s, what is its acceleration in ?sm 2 Express the answer in terms of "g's,"

0.56 g's

Billiard ball A of mass 𝑚𝐴 =0.400 kg moving with speed 𝑣𝐴 =1.80 𝑚 𝑠⁄ strikes ball B, initially at rest, of mass 𝑚𝐵 =0.500 kg. As a result of the collision, ball A is deflected off at an angle of 30.0º with a speed 𝑣′𝐴 =1.10 𝑚 𝑠⁄ . (a) Taking the x axis to be the original direction of motion of ball A, write down the equations expressing the conservation of momentum for the components in the x and y directions separately. (b) Solve these equations for the speed 𝑣′ 𝐵 and angle 𝜃′ 𝐵 of ball B. Do not assume the collision is elastic.

0.808 m/s at 330

What is the intensity of a sound at the pain level of 120 dB? Compare it to that of a whisper at 20 dB.

1.0 W/m2

A ball of mass 0.440 kg moving east (x+ direction) with a speed of 3.30 𝑚 𝑠⁄ collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?

1.10 m/s east, 4.40 m/s east

A 65.0-kg firefighter climbs a flight of stairs 20.0 m high. How much work is required?

1.27 X 10 4 J

What is the minimum work needed to push a 950-kg car 810 m up along a 9.0º incline? (a) Ignore friction. (b) Assume the effective coefficient of friction retarding the car is 0.25.

1.2X106 J, 3.0 X 106 J

A 9300-kg boxcar traveling at 15.0 𝑚 𝑠⁄ strikes a second boxcar at rest. The two stick together and move off with a speed of 6.0 𝑚 𝑠⁄ . What is the mass of the second car?

1.4X104 kg

During a workout, the football players at State U. ran up the stadium stairs in 66 s. The stairs are 140 m long and inclined at an angle of 32º. If a typical player has a mass of 95 kg, estimate the average power output on the way up. Ignore friction and air resistance.

1047 W

How much tension must a rope withstand if it is used to accelerate a 960-kg car horizontally along a frictionless surface at 1.20 m/s?

1150N

(a) What is the angular momentum of a figure skater spinning at 3.5 rev 𝑠⁄ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg? (b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?

14 kgm2, -2.7 mN

A centrifuge rotor has a moment of inertia of .mkg 1075.3 22 − How much energy is required to bring it from rest to 8250 rpm?

14,000 J

Calculate the force of Earth's gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth's surface if its mass is 1350 kg.

1470 N

A light plane must reach a speed of sm 33 for takeoff. How long a runway is needed if the (constant) acceleration is 3.0 m/s?

180 m

A fisherman notices that wave crests pass the bow of his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the waves traveling?

2.2 m/s

Water at a gauge pressure of 3.8 atm at street level flows into an office building at a speed of 0.60 𝑚 𝑠⁄ through a pipe 5.0 cm in diameter. The pipe tapers down to 2.6 cm in diameter by the top floor, 18 m above, where the faucet has been left open. Calculate the flow velocity and the gauge pressure in such a pipe on the top floor. Assume no branch pipes and ignore viscosity.

2.2 m/s, 2.0 atm

A 75-kg adult sits at one end of a 9.0-m-long board. His 25-kg child sits on the other end. (a) Where should the pivot be placed so that the board is balanced, ignoring the board's mass? (b) Find the pivot point if the board is uniform and has a mass of 15 kg

2.3 m from adult, 2.5 m from adult

The carton shown lies on a plane tilted at an angle º0.22= to the horizontal, with 𝜇𝑘 =0.12. (a) Determine the acceleration of the carton as it slides down the plane. (b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?

2.6 m/s2, 6.9 m/s

Two locomotives approach each other on parallel tracks. Each has a speed of hkm 95 with respect to the ground. If they are initially 8.5 km apart, how long will it be before they reach each other?

2.7 min

A baseball is hit nearly straight up into the air with a speed of .sm22 (a) How high does it go? (b) How long is it in the air?

25 m, 4.5 s

What is the maximum speed with which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?

25 m/s

A shotputter throws the shot with an initial speed of 15.5 m/s at a 34.0º angle to the horizontal. Calculate the horizontal distance traveled by the shot if it leaves the athlete's hand at a height of 2.20 m above the ground

25.6 m

How long will it take a 1750-W motor to lift a 315-kg piano to a sixth-story window 16.0 m above?

28.2 s

A geologist finds that a Moon rock whose mass is 9.28 kg has an apparent mass of 6.18 kg when submerged in water. What is the density of the rock?

2990 kg/m3

A device for training astronauts and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m. If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating? Express your answer in both 𝑚 𝑠⁄ and rev 𝑠⁄ .

30.4 m/s, 0.403 rev/sec

A hiker determines the length of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake.

343 m

In coming to a stop, a car leaves skid marks 92 m long on the highway. Assuming a deceleration of ,sm 00.7 2 estimate the speed of the car just before braking.

36 m/s

You buy a plastic dart gun, and being a clever physics student you decide to do a quick calculation to find its maximum horizontal range. You shoot the gun straight up, and it takes 4.0 s for the dart to land back at the barrel. What is the maximum horizontal range of your gun?

39 m

A box is given a push so that it slides across the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initial speed of 4.0 m/s.

4.1m

A person jogs eight complete laps around a quarter-mile track in a total time of 12.5 min. Calculate (a) the average speed and (b) the average velocity, in .s

4.3 m/s, 0 m/s

A helicopter is ascending vertically with a speed of .sm 20.5 At a height of 125 m above the Earth, a package is dropped from a window. How much time does it take for the package to reach the ground?

5.61 s

If you tried to smuggle gold ingots by filling your backpack, whose dimensions are 60 cm×28 cm×18 cm, what would its mass be?

580 kg =1,300 lbs

A novice skier, starting from rest, slides down a frictionless 35.0º incline whose vertical height is 185 m. How fast is she going when she reaches the bottom?

60.2 m/s

A softball player swings a bat, accelerating it from rest to 3.0 rev 𝑠⁄ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.

62 mN

What is the maximum acceleration a car can undergo if the coefficient of static friction between the tires and the ground is 0.80?

7.8 m/s2

What must be your car's average speed in order to travel 235 km in 3.25 h?

72.3 km/h

What force is needed to accelerate a child on a sled (total mass=60.0 kg) at ?sm 25.1 2

75.0N

Describe several situations in which an object is not in equilibrium, even though the net force on it is zero.

If the object has a net force on it of zero, then its center of mass does not accelerate. But since it is not in equilibrium, it must have a net torque, and therefore have an angular acceleration. Some examples1. Compact disk in a playrr as it comes to speed, after just bejng put in the player2. A hard drive on a computer when the computer is first turned on3. A window fan immediatley after the power has been shut off A bungee jumper momentarily comes to rest at the bottom of the dive before he springs back upward. At that moment, is the bungee jumper in equilibrium? Explain. The bungee jumper is not in equili

Explain the difference between the speed of a transverse wave traveling down a cord and the speed of a tiny piece of the cord.

In a transverse wave, the tiny piece moves up and down while the wave moves in a direction perpendicular to the tiny piece.

A projectile is launched at an angle of 30º to the horizontal with a speed of .sm 30 How does the horizontal component of its velocity 1.0 s after launch compare with its horizontal component of velocity 2.0 s after launch?

In projectile motion, horizontal component of velocity remains constant as there is no acceleration in horizontal direction.And, horizontal component of velocity1.0s after launch is equal to its horizontal component of velocity 2.0s after launch.

child wishes to determine the speed a slingshot imparts to a rock. How can this be done using only a meter stick, a rock, and the slingshot?

Launch the rock with a horizontal velocity from a known height over level ground. Use the equations for projectile motion in the y-direction to find the time the rock is in the air. (Note that the initial velocity has a zero y-component.) Use this time and the horizontal distance the rock travels in the equation for x-direction projectile motion to find the speed in the x-direction, which is the speed the slingshot imparts. The meter stick is used to measure the initial height and the horizontal distance the rock travels.

Why are the frets on a guitar spaced closer together as you move up the fingerboard toward the bridge?

Recalling that the length of a string plucked is related to the pitch it produces and frets are responsible of making the pitch increase. This is why as you move up the fingerboard toward the bridge, the spacing of the frets gets smaller.

Give several everyday examples of resonance.

Resonance can occur in any system that has a natural frequency. You probably have experienced a rattle or buzz in your car that only occurs at a certain speed. This is an example of resonance; the tires provide a periodic driving force which changes frequency as you change speed.

Standing waves can be said to be due to "interference in space," whereas beats can be said to be due to "interference in time." Explain.

Standing waves can be said to be due to "interference in space" whereas beats can be said to be due to "interference in time" explain. The wave pattern created by standing waves does not travel from one place to another. The node location safe fixed in space. Any one point in medium has the same amplitude at all times.

When a sinusoidal wave crosses the boundary between two sections of cord as in Fig. 11-33, the frequency does not change (although the wavelength and velocity do change). Explain why.

The frequency must stay the same because the media is continuous - the end of one section of cord is physically tied to the other section of cord.

A block is given a push so that it slides up a ramp. After the block reaches its highest point, it slides back down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

The kinetic friction force is parallel to the ramp and the block's weight has a component parallel to the ramp.

The gravitational force on the Moon due to the Earth is only about half the force on the Moon due to the Sun. Why isn't the Moon pulled away from the Earth?

The moon is not pulled away from the earth because the moon and the earth are experiencing nearly the same radial acceleration due to the sun.

Two solid spheres simultaneously start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

This speed is independent of the mass and radius of the ball, and so both balls will have the same speed at the bottom. In fact, this is true for ANY height of fall, so the two balls will have identical instantaneous speeds all along their descent, and so both balls will take the same time to reach the bottom. The ball with the larger mass has the greater total kinetic energy. Another way to consider this is that the initial potential energy of Mgh is all converted to kinetic energy. The larger mass has more potential energy to begin with (due to the larger mass), and so has more kinetic energy at the bottom.

Why do tightrope walkers carry a long, narrow beam?

Tightrope walkers carry a long narrow beam to help them balance by increasing their rotational inertia.

When a sound wave passes from air into water, do you expect the frequency or wavelength to change?

When it travels from air to water, its source remains the same and the length of a second does not change, So, the frequency remains constant.

When will your apparent weight be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

When the elevator is accelerating upwards, the total force on the body will be in an upward direction. So, the normal force exerted on the body will be higher than its weight, and the reading scale will indicate the greatest apparent weight. When the elevator is in free-fall motion, the body, as well as the elevator, is accelerating in the downward direction, which means that the normal force will be zero. Hence, the apparent weight is equal to zero. When the elevator is accelerating in the upward direction with a constant speed, then the normal force (N) on the body is equivalent to the body's weight (mg). So, in this condition, the apparent weight of the body will be the same as standing on the ground.

Will the acceleration of a car be the same when the car travels around a sharp curve at a constant hkm 60 as when it travels around a gentle curve at the same speed? Explain.

When the vehicle is moving in a sharp curve, the radius will be smaller, and acceleration will be higher. On the contrary, the acceleration will be lower if the car is traveling in a gentle curve.

Is the frequency of a simple periodic wave equal to the frequency of its source? Why or why not?

Yes. A simple periodic wave travels through a medium, which must be in contact with or connected to the source for the wave to be generated.

An airplane is traveling 735 km/h in a direction 41.5º west of north. (a) Find the components of the velocity vector in the northerly and westerly directions. (b) How far north and how far west has the plane traveled after 3.00 h?

a) 487 km/h (b) 1650 km (north), 1460 km (west)

A squash ball hits a wall at a 45º angle as shown. What is the direction (a) of the change in momentum of the ball, (b) of the force on the wall?

a) Assuming speed remains constant, the momentum in the y direction will not change. The final momentum will have a negative x-component while the initial momentum had a positive x-component.(b)A ball feels a force with the negative x direction thus by Newton's Third Law the ball feels a force in the positive x direction

A stone is thrown vertically upward with a speed of sm 0.12 from the edge of a cliff 70.0 m high. (a) How much later does it reach the bottom of the cliff? (b) What is its speed just before hitting? (c) What total distance did it travel?

a)5.20 s (b) 38.9 m/s (c) 84.7 m

As a freely falling object speeds up, what is happening to its acceleration due to gravity — does it increase, decrease, or stay the same?

acceleration stays the same

Can two vectors of unequal magnitude add up to give the zero vector? Can three unequal vectors? Under what conditions?

for two vectors of unequal magnitude, their vector sum cannot be a zero vector. if out of three, the sum of any two vectors is equal to the negative of the third vector, then the vector sum of all three vectors will be zero, even when all the vectors are different.

A light object and a heavy object have the same kinetic energy. Which has the greater momentum? Explain.

heavy object will have greater momentum as its mass will be greater.

If the acceleration of an object is zero, are no forces acting on it? Explain.

no, all the forces acting on the object equal zero

Why do you float higher in salt water than in fresh?

saltwater gives more buoyancy than freshwater because of the higher density of saltwater

Does a car speedometer measure speed, velocity, or both?

speed, velocity must have a directions