The position of a particle moving along an x axis is given by x = 16.0t² - 6.00t³, where x is in meters and t is in seconds. Determine (a) the position, (b) the velocity, and (c) the acceleration of the particle at t = 3.00 s. (d) What is the maximum positive coordinate reached by the particle and (e) at what time is it reached? (f) What is the maximum positive velocity reached by the particle and (g) at what time is it reached? (h) What is the acceleration of the particle at the instant the particle is not moving (other than at t = 0)? (i) Determine the average velocity of the particle between t = 0 and t = 3.00 s.

a)number

b)number

C)number

D)number

E)number

F)number

g)number

H)number

i)number

You drive on Interstate 10 from San Antonio to Houston, half the time at 63 km/h and the other half at 90 km/h. On the way back you travel half the distance at 63 km/h and the other half at 90 km/h. What is your average speed (a) from San Antonio to Houston, (b) from Houston back to San Antonio, and (c) for the entire trip? (d) What is your average velocity for the entire trip?

a)number

b)number

c)number

d)number

The magnetic field 39.0 cm away from a long, straight wire carrying current 4.00 A is 2050 nT.

(a) At what distance is it 205 nT?
cm

(b) At one instant, the two conductors in a long household extension cord carry equal 4.00-A currents in opposite directions. The two wires are 3.00 mm apart. Find the magnetic field 39.0 cm away from the middle of the straight cord, in the plane of the two wires.
nT

(c) At what distance is it one-tenth as large?
cm

(d) The center wire in a coaxial cable carries current 4.00 A in one direction, and the sheath around it carries current 4.00 A in the opposite direction. What magnetic field does the cable create at points outside the cables?
nT

A disk turns through an angle of β(t)=Ct² - Bt³ where C=3.20 rad/s² and B= 0.500 rad/s³.
Calculate the angular acceleration α(t) and velocity w(t) as a function of time.

Isolated molecular clouds can have a temperature as low as 20 K and a particle density as great as 1.2×10⁵ per cubic centimeter.

What is the minimum mass that a cloud with these properties needs in order to form a star?

Mcloud= _________ MSun

The coefficient of friction (static and kinetic) between an object and a surface can be measured by putting the object on an adjustable inclined plane. (a) Draw a free-body diagram for the object, assuming static friction holds it in place on the incline. (b) Find an equation that can be used to solve for µs, in terms of the angle θmax which is the largest angle that the object can sit without sliding. (Hint: You can reduce the problem to two unknowns—the magnitude of ~n and the coefficient µs—so you will need two equations to solve for them both. Newton’s 2nd Law can provide both equations, since there are forces in both the x and y directions.) (c) Find the angle θconst where the object will move with a constant velocity down the incline if it is given an initial push. (d) Which is bigger, θconst or θmax? Describe the motion of the object (e.g., is it speeding up, slowing down, etc.) for each range of θ: between 0 and the smaller special angle, between the two special angles, and between the larger special angle and 90◦ . (Hint: You can check your answer with an experiment; a textbook cover provides a decent adjustable incline.)

Friends Mercedes and Kaandra are working out together at the 400 m track. Kaandra can do the 1600 m in a blazing 5 minutes and 30 seconds. Mercedes is significantly slower doing that distance in 7 minutes. The women decide to have a race going twice around the track. To make it more competitive Kaandra gives Mercedes a 100 m head start (i.e. Mercedes only runs 700 m). Who wins, by how much time?

An insulated tank is divided into two parts by a partition as shown in the figure. One part of the tank contains 2.5 kg of compressed liquid water at 60°C and 600 kPa while the other part is evacuated. The partition is now removed, and the water expands to fill the entire tank. Determine the final temperature of the water and the volume of the tank for a final pressure of 3 kPa. (Round the final temperature to two decimal places and round the final volume to three decimal places.)

In a student experiment, a constant-volume gas thermometer is calibrated in liquid nitrogen (−196°C) and in boiling pentane (36.1°C). The separate pressures are 0.347 atm and 1.436 atm. Hint: Use the linear relationship P = A + BT, where A and B are constants.

(a) What value of absolute zero does the calibration yield?
°C

(b) What pressure would be found at the freezing point of water?
atm

(c) What pressure would be found at the boiling point of water?
atm

A hollow aluminum cylinder 22.5 cm deep has an internal capacity of 2.000 L at 15.0°C. It is completely filled with turpentine at 15.0°C. The turpentine and the aluminum cylinder are then slowly warmed together to 65.0°C. (The average linear expansion coefficient for aluminum is 24 ✕ 10⁻⁶°C⁻¹, and the average volume expansion coefficient for turpentine is 9.0 ✕ 10⁻⁴°C⁻¹.)

(a) How much turpentine overflows?
cm³

(b) What is the volume of turpentine remaining in the cylinder at 65.0°C? (Give your answer to at least four significant figures.)
L

(c) If the combination with this amount of turpentine is then cooled back to 15.0°C, how far below the cylinder's rim does the turpentine's surface recede?
cm

9) Consider a 4.00 C charge. What is the magnitude of the electric field it creates 2.56 m directly up from it?

10) Which direction is this electric field pointed? Select one: Right, Down, Left, Up

11) Consider a -4.00 C charge. What is the magnitude of the electric field it creates 2.56 m directly down from it?

12) Which direction is this electric field pointed? Select one: Up, Left, Right, Down

13) An electric field of intensity 3.50*10³ N/C is applied along the x-axis. Calculate the electric flux through a rectangular plan 0.489 m and 0.700 m long if the plane is parallel to the yz-plane (x-axis is perpendicular to it).

14) A charged particle A exerts a force of 4.68 N to the right on an electron (q=-e=-1.6*10^-19 C) which is 13.7 mm from it. What is the magnitude of the charge of particle A?

A 1450 kg car begins sliding down a 12.0 ° inclined road with a speed of 34.0 km/h.The engine is turned off, and the only forces acting on the car are a net frictional force from the road and the gravitational force. After the car has traveled 45.0 m along the road, its speed is 50.0 km/h. (a) How much is the mechanical energy of the car reduced because of the net frictional force? (b) What is the magnitude of that net frictional force?

Consult Interactive Solution 21.51 to see how this problem can be solved. A coil rotating perpendicularly to a uniform magnetic field contains 340 turns and has an area per turn of 3.0 × 10^-3 m². The magnetic field is 0.18 T, and the current in the coil is 0.15 A. A brake shoe is pressed perpendicularly against the shaft to keep the coil from turning. The coefficient of static friction between the shaft and the brake shoe is 0.79. The radius of the shaft is 0.0077 m. What is the magnitude of the minimum normal force that the brake shoe exerts on the shaft?

Consider three point charges q1=q2=q3=Q. If q1 and q2 are located on the Y-axis at y=+a and y= -a and the third charge is located at a point x on the X-axis. (a) find the force E exerted by q1 and q2 on q3 when q3 is located at the origin (b) what is the force F on q3 when q3 is located at an arbitrary value of x on the X-axis? (c) for what value of x is the force F on q3 a maximum? Hint. The notation F means that you need to find the magnitude and direction of the electric force.

The magnetic field 38.0 cm away from a long, straight wire carrying current 4.00 A is 2110 nT.

(a) At what distance is it 211 nT?

380 cm

(b) At one instant, the two conductors in a long household extension cord carry equal 4.00-A currents in opposite directions. The two wires are 3.00 mm apart. Find the magnetic field 38.0 cm away from the middle of the straight cord, in the plane of the two wires.

16.6 nT

(c) At what distance is it one-tenth as large?

_______________________cm

(d) The center wire in a coaxial cable carries current 4.00 A in one direction, and the sheath around it carries current 4.00 A in the opposite direction. What magnetic field does the cable create at points outside the cables?
0 nT

Derive the general wavefunction for a particle in a box (i.e. the infinite square well

potential). Go on to normalise it. What energy/energies must the particle have to

exist in this box?