An object of mass \(3 \ kg\) moves with a speed of \(4 \ m/s\) when seen from the ground, while it moves with a speed of \(2 \ m/s\) when seen from a bicycle. What is the difference in the kinetic energies seen by both the frames of reference?

A boy pulls a toy car initially at rest with a force \(\overrightarrow{F}\), as shown below.

As a result, the toy car accelerates uniformly for time \(t\). What is the work done on the car by the boy in time \(t\)? (Assume the mass of the car is \(m\).)

Zack releases an object of mass \(4\ kg\) from a height of 6 m from the ground level. The object loses \(15\ J\) of energy due to frictional forces acting on it. What is the velocity when the object reaches the other side of the curve?

A car of mass \(1500 \ kg\) has broken down on the side of a flat road. The owner pushes the car to the side of the road, causing the car to accelerate from rest to a speed of \(2 \ m/s\) in 5 seconds. What is the person’s average power output while they are pushing?

An object of mass \(M\) compresses the length of a spring by \(y\). It is then released, and the object thus travels a distance \(l\) on a rough surface. If the spring is compressed by \(4y\), then the distance travelled by the object would be,

A position-dependent force \(F\) acts on a 1D system, as shown below.

What is the work done on the system by the position-dependent force?

Hannah sets a conical pendulum in motion. The radius of the pendulum is \(l\), its speed is \(v\), and the length of the string is \(5l\).

What is the work done by the tension force on the pendulum?

A simple pendulum is constructed using a thin, light string of length \(5L\) and a metal ball of mass \(m\). The pendulum is initially pulled back so that the metal ball is a distance \(3L\) from vertical and released (see figure 1 above). The metal ball passes through the lowest point in the pendulum path traveling with speed \(v_1\). Later, the mass is pulled back to a greater angle so that the mass is initially a distance \(4L\) from vertical, then released (see figure 2 above). In this case, the mass reaches a maximum speed of \(v_2\). What is the ratio of \(v_1\) to \(v_2\)?

A block of mass \(2.4\ kg\) is sliding down a rough incline plane at a constant speed of \(4\ m/s\).

The angle of the incline with the horizontal is \(30°\). What is the power delivered by the gravitational force on the block?

Which of the below graphs shows the kinetic energy of a mass attached to a spring as a function of its position?

A block of mass \(1.5\ kg\) is moving at a speed of \(3.5\ m/s\). It suddenly passes through a rough patch, and its speed decreases to \(2\ m/s\) after coming out from the patch. In what form has the kinetic energy of the block converted into, and how much?

Chole throws two stones of different masses, horizontally with a speed of \(10\ m/s\) and \(14\ m/s\), respectively. She is standing at a height of \(
5\ m\) from the ground. Which of these below statements is correct?

A simple pendulum swings with a time period of \(t\ sec\). Which of the below statements regarding the pendulum is incorrect?

(Assume there is no air drag acting on the pendulum.)

An arrow is traveling horizontally when it collides with and sticks to a block of wood. The arrow and block travel at a speed \(v\) immediately after the collision, and reach a maximum height of \(h_1\) above the block’s initial position as they swing upward. Later, the same arrow is traveling at a greater speed when it collides with the same block. After this second collision, the block and arrow are traveling at a speed of \(2_v\). What is the maximum height reached by the block and arrow in this second collision in terms of \(h_1\)?

A car loses its break and needs to slow down to prevent an accident. The driver takes the car on a rough patch so that it slows down due to frictional forces. The mass of the car is \(1{,}700\ kg\) and the initial velocity of the car is \(25\ m/s\). It takes the car \(80\ s\) to stop completely. What is the average power delivered to the car by the frictional forces?