A sled of mass m is given a kick on a frozen pond. The kick imparts to the sled an initial speed of v. The coefficient of kinetic friction between sled and ice is $\mu_{k}.$ Use energy considerations to find the distance the sled moves before it stops.

Given that at time $t_i$, the kinetic energy of a particle is $30.0 \mathrm{~J}$ and the potential energy of the system to which it belongs is $10.0 \mathrm{~J}$. At some later time $t_f$, the kinetic energy of the particle is $18.0 \mathrm{~J}$. If the potential energy of the system at time $t_f$ is $5.00 \mathrm{~J}$, are there any nonconservative forces acting on the particle? Explain.

Given that at time $t_i$, the kinetic energy of a particle is $30.0 \mathrm{~J}$ and the potential energy of the system to which it belongs is $10.0 \mathrm{~J}$. At some later time $t_f$, the kinetic energy of the particle is $18.0 \mathrm{~J}$. If the potential energy of the system at time $t_f$ is $5.00 \mathrm{~J}$, are there any nonconservative forces acting on the particle?

At time $t_{i},$ the kinetic energy of a particle is 30.0 J and the potential energy of the system to which it belongs is 10.0 J. At some later time $t_{f}$, the kinetic energy of the particle is 18.0 J. (a) If only conservative forces act on the particle, what are the potential energy and the total energy of the system at time $t_{f}$? (b) If the potential energy of the system at time $t_{f}$ is 5.00 J, are any nonconservative forces acting on the particle? (c) Explain your answer to part (b).

A $2000-\mathrm{kg}$ car moves down a level highway under the actions of two forces: a $1000-\mathrm{N}$ forward force exerted on the drive wheels by the road and a $950-\mathrm{N}$ resistive force. Use the work-energy theorem to find the speed of the car after it has moved a distance of $20 \mathrm{~m}$, assuming that it starts from rest.

A $0.60-\textrm{kg}$ particle has a speed of $2.0 \textrm{m/s}$ at point A and kinetic energy of $7.5 \textrm{ J}$ at point B. What is The total work done on the particle as it moves from A to B?

A block of mass 0.250 kg is placed on top of a light, vertical spring of force constant 5000 N/m and pushed downward so that the spring is compressed by 0.100 m. After the block is released from rest, it travels upward and then leaves the spring. To what maximum height above the point of release does it rise?

A 0.60-kg particle has a speed of 2.0 m/s at point A and a kinetic energy of 7.5 J at point B. What is Its speed at point B?

A 0.60-kg particle has a speed of 2.0 m/s at point A and a kinetic energy of 7.5 J at point B. What is its kinetic energy at A?

A particle is subject to a force $F_{x}$ that varies with position. Find the work done by the force on the particle as it moves (a) from x = 0 to x = 5.00 m, (b) from x = 5.00 m to x = 10.0 m, and (c) from x = 10.0 m to x = 15.0 m. (d) What is the total work done by the force over the distance x = 0 to x = 15.0 m?

A $2.0 \mathrm{~g}$ bullet leaves the barrel of a gun at a speed of $300 \mathrm{~m} / \mathrm{s}$. (b) Find the average force exerted by the expanding gases on the bullet as it moves the length of the 50 -cm-long barrel.

A $2.0 \mathrm{~g}$ bullet leaves the barrel of a gun at a speed of $300 \mathrm{~m} / \mathrm{s}$. (a) Find its kinetic energy.

An inclined plane of angle $\theta=20.0^{\circ}$ has a spring of force constant k = 500 N/m fastened securely at the bottom so that the spring is parallel to the surface. A block of mass m = 2.50 kg is placed on the plane at a distance d = 0.300 m from the spring. From this position, the block is projected downward toward the spring with speed v = 0.750 m/s. By what distance is the spring compressed when the block momentarily comes to rest?

The force acting on a particle varies. Find the work done by the force on the particle W as it moves
(c) from $x=0$ to $x=10.0 \mathrm{~m}$.