Starting from a pillar, you run a distance 200 m east (the +x-direction) at an average speed of 5.0 m/s, and then run a distance 280 m west at an average speed of 4.0 m/s to a post. Part A Calculate your average speed from pillar to post. Express your answer in meters per second. vav = m/s Submit Request Answer Part B Calculate your average velocity from pillar to post. Express your answer in meters per second.
A Honda Civic travels in a straight line along a road. Its distance x from a stop sign is given as a function of time t by the equation x(t) = αt2 − βt3, where α = 1.45 m/s2 and β = 0.0510 m/s3. Part A Calculate the average velocity of the car for the time interval t = 0 to t = 2.10 s. Express your answer in meters per second. m/s Part B Calculate the average velocity of the car for the time interval t = 0 to t = 3.90 s. Express your answer in meters per second. Submit Request Answer Part C Calculate the average velocity of the car for the time interval t = 2.10 s to t = 3.90 s. Express your answer in meters per second.
A car is stopped at a traffic light. It then travels along a straight road so that its distance from the light is given by x(t) = bt2 − ct3, where b = 3.00 m/s2 and c = 0.130 m/s3. For related problemsolving tips and strategies, you may want to view a Video Tutor Solution of Average and instantaneous velocities. Part A Calculate the average velocity of the car for the time interval t = 0 to t = 10.0 s. Express your answer in meters per second. Part B Calculate the instantaneous velocity of the car at t = 0. Express your answer in meters per second. Submit Request Answer Part C Calculate the instantaneous velocity of the car at t = 5.00 s. Express your answer in meters per second. Part D Calculate the instantaneous velocity of the car at t = 10.0 s. Express your answer in meters per second. Submit Request Answer Part E How long after starting from rest is the car again at rest? Express your answer in seconds. t = s
A ball moves in a straight line (the x-axis). The graph in the figure (Figure 1) shows this ball's velocity as a function of time. For related problemsolving tips and strategies, you may want to view a Video Tutor Solution of Average and instantaneous velocities. Figure 1 of 1 Part A What is the ball's average velocity during the first 2.7 s ? Express your answer in meters per second. Submit Request Answer Part B What is the ball's average speed during the first 2.7 s ? Express your answer in meters per second. vav = m/s Part C Suppose that the ball moved in such a way that the graph segment after 2.0 s was −3.0 m/s instead of +3.0 m/s. Find the ball's average velocity during the first 2.7 s in this case. Express your answer in meters per second. vav = m/s Submit Request Answer Part D Find the ball's average speed during the first 2.7 s in the case described in part C. Express your answer in meters per second.
A race car starts from rest and travels east along a straight and level track. For the first 5.0 s of the car's motion, the eastward component of the car's velocity is given by vx(t) = (0.990 m/s3)t2. Part A What is the acceleration of the car when vx = 12.5 m/s ? Express your answer with the appropriate units.
An astronaut has left the International Space Station to test a new space scooter. Her partner measures the following velocity changes, each taking place in a 12 s interval. What is the average acceleration in each interval? Assume that the positive direction is to the right. Part A At the beginning of the interval, the astronaut is moving toward the right along the x-axis at 15.3 m/s, and at the end of the interval she is moving toward the right at 4.6 m/s. Express your answer in meters per second squared. Part B At the beginning she is moving toward the left at 4.6 m/s, and at the end she is moving toward the left at 15.3 m/s. Express your answer in meters per second squared. a = m/s2 Submit Request Answer Part C At the beginning she is moving toward the right at 15.3 m/s, and at the end she is moving toward the left at 15.3 m/s. Express your answer in meters per second squared.
An antelope moving with constant acceleration covers the distance 70.0 m between two points in time 6.00 s. Its speed as it passes the second point is 14.0 m/s. Part A What is its speed at the first point? Express your answer with the appropriate units. Submit Request Answer Part B What is the acceleration? Express your answer with the appropriate units.
The fastest measured pitched baseball left the pitcher's hand at a speed of 49.0 m/s. The pitcher was in contact with the ball over a distance of 1.50 m and produced constant acceleration. For related problemsolving tips and strategies, you may want to view a Video Tutor Solution of Constant-acceleration calculations Part A What acceleration did he give the ball? Express your answer in meters per second squared. Submit Request Answer Part B How much time did it take him to pitch it? Express your answer in seconds. t =
For related problemsolving tips and strategies, you may want to view a Video Tutor Solution of Up-and-down motion in free fall. Part A If a flea can jump straight up to a height of 0.540 m, what is its initial speed as it leaves the ground? Express your answer in meters per second. Submit Request Answer Part B How long is it in the air? Express your answer in seconds. t = s
A 15 kg rock is dropped from rest on the earth and reaches the ground in 1.75 s. When it is dropped from the same height on Saturn's satellite Enceladus, it reaches the ground in 18.6 s. For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of A freely falling coin. Part A What is the acceleration due to gravity on Enceladus? Express your answer with the appropriate units.
A ball starts from rest and rolls down a hill with uniform acceleration, traveling 100 m during the second 5.6 s of its motion. Part A How far did it roll during the first 5.6 s of motion? Express your answer with the appropriate units. d =
You are standing at rest at a bus stop. A bus moving at a constant speed of 5.00 m/s passes you. When the rear of the bus is 19.0 m past you, you realize that it is your bus, so you start to run toward it with a constant acceleration of 0.960 m/s2. Part A How far would you have to run before you catch up with the rear of the bus? Express your answer with the appropriate units. Part B How fast must you be running then? Find the final speed just as you reach the bus. Express your answer with the appropriate units. Submit Request Answer Part C Would an average college student be physically able to accomplish this? Yes No
The charge density on a disk of radius R = 12.2 cm is given by σ = ar, with a = 1.42 μC/m3 and r measured radially outward from the origin (see figure below). What is the electric potential at point A, a distance of 42.0 cm above the disk? Hint: You will need to integrate the nonuniform charge density to find the electric potential. You will find a table of integrals helpful for performing the integration. Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. V
A total electric charge of 2.50 nC is distributed uniformly over the surface of a metal sphere with a radius of 18.0 cm. The potential is zero at a point at infinity. Part A Find the value of the potential at 50.0 cm from the center of the sphere. Express your answer in volts. Submit Request Answer Part B Find the value of the potential at 18.0 cm from the center of the sphere. Express your answer in volts. V = Submit Request Answer Part C Find the value of the potential at 14.0 cm from the center of the sphere. Express your answer in volts. V = V
Two protons are released from rest when they are 0.750 nm apart. Part A What is the maximum speed they will reach? Submit Request Answer Part B What is the maximum acceleration they will achieve?
Part A An electron is to be accelerated from a velocity of 2.00×106 m/s to a velocity of 7.50×106 m/s. Through what potential difference must the electron pass to accomplish this? Express your answer in volts. Submit Request Answer Part B Through what potential difference must the electron pass if it is to be slowed from 7.50×106 m/s to a halt? Express your answer in volts.
Part A An infinitely long line of charge has linear charge density 5.00×10−12 C/m. A proton (mass 1.67×10−27 kg, charge e ) is 18.0 cm from the line and moving directly toward the line at 3000 m/s. Calculate the proton's initial kinetic energy. Express your answer numerically in joules to four significant figures. Submit Request Answer Part B How close does the proton get to the line of charge? Express your answer numerically in meters to three significant figures.
A target is made in the form of a circular disk of radius R. A total positive charge Q is spread uniformly over the target. Part A Find the electrostatic potential at a point on the axis of the target and a positive distance z away from its center. Write your answer in terms of z, Q, R and ϵ0. Submit Request Answer Part B You stand a long way from the target and shoot a bullet with mass m and carrying a positive charge q straight at the center of the bullseye (ignore gravity). Find the minimum speed vmin with which the bullet must leave the gun in order for the bullet to reach the target. Write your answer in terms of Q, q, R, m and ϵ0.
A very long insulating cylindrical shell of radius 6.80 cm carries charge of linear density 8.70 μC/m spread uniformly over its outer surface. For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of An infinite line charge or charged conducting cylinder Part A What would a voltmeter read if it were connected between the surface of the cylinder and a point 4.50 cm above the surface? Express your answer in volts. Submit Request Answer Part B What would a voltmeter read if it were connected between the surface and a point 1.00 cm from the central axis of the cylinder? Express your answer in volts.
The figure (Figure 1) shows eight point charges arranged at the corners of a cube with sides of length d. The values of the charges are +q and −q, as shown. This is a model of one cell of a cubic ionic crystal. In sodium chloride ( NaCl), for instance, the positive ions are Na+ and the negative ions are Cl−. Figure 1 of 1 Part A Calculate the potential energy U of this arrangement. (Take as zero the potential energy of the eight charges when they are infinitely far apart. ) Express your answer in terms of the given quantities and appropriate constants. U = Submit Request Answer
Two spherical shells have a common center. The inner shell has radius R1 = 5.00 cm and charge q1 = +2.00×10−6 C; the outer shell has radius R2 = 15.0 cm and charge q2 = −5.00×10−6 C. Both charges are spread uniformly over the shell surface. Take V = 0 at a large distance from the shells. Part A What is the electric potential due to the two shells at the distance r = 2.50 cm from their common center. Express your answer with the appropriate units. Part B What is the electric potential due to the two shells at the distance r = 10.0 cm from their common center. Express your answer with the appropriate units. Submit Request Answer Part C What is the electric potential due to the two shells at the distance r = 20.0 cm from their common center. Express your answer with the appropriate units.
A small sphere with mass 2.90 g hangs by a thread between two large parallel vertical plates 5.00 cm apart ( Figure 1). The plates are insulating and have uniform surface charge densities +σ and −σ. The charge on the sphere is q = 7.60×10−6 C. Figure 1 of 1 Part A What potential difference between the plates will cause the thread to assume an angle of 30.0∘ with the vertical? Express your answer in volts. Submit Request Answer
A Geiger counter detects radiation such as alpha particles by using the fact that the radiation ionizes the air along its path. A thin wire lies on the axis of a hollow metal cylinder and is insulated from it (Figure 1). A large potential difference is established between the wire and the outer cylinder, with the wire at higher potential; this sets up a strong electric field directed radially outward. When ionizing radiation enters the device, it ionizes a few air molecules. The free electrons produced are accelerated by the electric field toward the wire and, on the way there, ionize many more air molecules. Thus a current pulse is produced that can be detected by appropriate electronic circuitry and converted to an audible "click." Suppose the radius of the central wire is 145 μm and the radius of the hollow cylinder is 1.80 cm. Part A What potential difference between the wire and the cylinder produces an electric field of 2.00×104 V/m at a distance of 1.20 cm from the axis of the wire? (Assume that the wire and cylinder are both very long in comparison to their radii.) Submit Request Answer Figure 1 of 1
The position of a squirrel running in a park is given by Part A What is vx(t), the x-component of the velocity of the squirrel, as a function of time? r→ = [(0.280 m/s)t + (0.0360 m/s2)t2]i^ + (0.0190 m/s3)t3 j^. vx(t) = (0.0720 m/s2)t vx(t) = 0.280 m/s vx(t) = (0.280 m/s)t + (0.0360 m/s2)t2 vx(t) = 0.280 m/s + (0.0720 m/s2)t Part B What is vy(t), the y-component of the velocity of the squirrel, as a function of time? vy(t) = (0.0570 m/s2)t2 vy(t) = (0.0570 m/s3)t vy(t) = (0.0570 m/s3)t + (0.0720 m/s2)t2 vy(t) = (0.0570 m/s3)t2 Submit Request Answer Part C At t = 5.40 s, how far is the squirrel from its initial position? Express your answer with the appropriate units. r = Value Units Part D At t = 5.40 s, what is the magnitude of the squirrel's velocity? Express your answer with the appropriate units. v = Value Units Units Submit Request Answer Part E At t = 5.40 s, what is the direction (in degrees counterclockwise from +x-axis) of the squirrel's velocity? Express your answer in degrees.
A jet plane is flying at a constant altitude. At time t1 = 0 it has components of velocity vx = 90 m/s, vy = 105 m/s. At time t2 = 35.0 s the components are vx = 175 m/s, vy = 40 m/s. Part A For this time interval calculate the average acceleration. Express your answers in meters per second squared separated by a comma. ax, ay = m/s2 Part B Find the magnitude of the average acceleration. Express your answer in meters per second squared. aav = m/s2 Submit Request Answer Part C Find the direction of the average acceleration (let the direction be the angle that the vector makes with the +x axis, measured counterclockwise). Express your answer in degrees. θ =
A daring 510 N swimmer dives off a cliff with a running horizontal leap, as shown in (Figure 1). Figure 1 of 1 Part A What must her minimum speed be just as she leaves the top of the cliff so that she will miss the ledge at the bottom, which is 1.75 m wide and 9.00 m below the top of the cliff? Express your answer with the appropriate units. v0
A man stands on the roof of a building of height 14.0 m and throws a rock with a velocity of magnitude 34.0 m/s at an angle of 26.0∘ above the horizontal. You can ignore air resistance. Part A Calculate the maximum height above the roof reached by the rock. Express your answer in meters. Part B Calculate the magnitude of the velocity of the rock just before it strikes the ground. Express your answer in meters per second. v = m/s Submit Request Answer Part C Calculate the horizontal distance from the base of the building to the point where the rock strikes the ground. Express your answer in meters.
The radius of the earth's orbit around the sun (assumed to be circular) is 1.50×108 km, and the earth travels around this orbit in 365 days. Part A What is the magnitude of the orbital velocity of the earth in m/s ? Express your answer in meters per second. Part B What is the radial acceleration of the earth toward the sun? Express your answer in meters per second squared. Submit Request Answer Part C What is the magnitude of the orbital velocity of the planet Mercury (orbit radius = 5.79×107 km, orbital period = 88.0 days )? Express your answer in meters per second.
A "moving sidewalk" in an airport terminal building moves at a speed of 1.4 m/s and is of length 39.0 m. A woman steps on at one end and walks at a speed 1.8 m/s relative to the moving sidewalk. For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Relative velocity on a straight road. Part A How much time does she require to walk from one end to the other if she walks in the same direction the sidewalk is moving? Express your answer in seconds. Submit Request Answer Part B How much time does she require to walk from one end to the other if she walks opposite to the direction the sidewalk is moving? Express your answer in seconds. t = s
The nose of an ultralight plane is pointed south, and its airspeed indicator shows 41 m/s. The plane is in a 17 m/s wind blowing toward the southwest relative to the earth. For help with math skills, you may want to review: Vector Addition Resolving Vector Components For general problem-solving tips and strategies for this topic, you may want to view a Video Tutor Solution of Flying in a crosswind. Part A Letting x be east and y be north, find the components of v→P/E (the velocity of the plane relative to the earth). Express your answers in meters per second separated by a comma. View Available Hint(s) Submit Part B Find the magnitude of v→P/E. Express your answer in meters per second. View Available Hint(s) vP/E = m/s