A boy pedals a cycle to reach a speed of $6 \ m/s$. The force needed to keep the cycle moving at the same speed is $40 \ N$. What is the power delivered by the boy to keep the cycle moving forward?

(Assume the angle between the velocity and the force is 0°.)

A position-dependent force (in 1D) acts on an object of mass $m$. The graph shows the variation in the force as the object displaces from its initial position.

What is the total work done by the force on the object?

A particle of mass $0.5 \ kg$ is at rest and is constrained to move parallel to the $y-axis$. If a force of $(10\skew{2.5}\hat{i} + 6\skew{4}\hat{j} \ ) \ N$ starts acting on the object from $t=0 \ s$, what is the work done on the object from $t=0 \ s$ to $t=4 \ s$?

A block at rest is pulled by a force acting at an angle of $60°$ with the horizontal. The block displaces by $23 \ m$ horizontally without being accelerated by the force. If the work done by the force is $230 \ J$, what is the force acting on the block?

A heavy block moving on a table decelerates due to the frictional force.

The block’s speed changes from $15 \ m/s$ to $3 \ m/s$ in $5 \ s$. If the weight of the block is equal to $100 \ N$, what is the coefficient of kinetic friction between the block and the table?

Two blocks are resting on a frictionless inclined plane, as shown below.

What is the change in the total kinetic energy of the two-block system when the left block reaches the pulley after being allowed to move from the above configuration?

(Here, $g$ is the acceleration due to gravity)

The net force acting on an object is given by the equation,

$f(x)=(2x+1) \ N$

What is the change in the kinetic energy of the system when the object moves from $x=2 \ m$ to $x=6 \ m$?

A toy of mass $0.2 \ kg$ is left from the top of a pre-determined track of height $h \ m$.

The track has a single circular loop of diameter $3 \ m$ after the curve. What is the minimum height from which the toy should be left so that it completes the circle without losing contact at any point on it?

George sets a pendulum in motion from point $C$. The length of the pendulum is equal to $2 \ m$, and the mass attached to the pendulum is $0.5 \ kg$.

What is the tension force acting on the mass when it is at point $A$?

Questions 10 and 11 are based on the below information:

A weird positional dependent frictional force acts on a block sliding down from the top of an inclined plane of slanting length $10 \ m$ and height $5 \ m$. The dependence of the frictional force on the position is given as $f_r (x)=A \sqrt{x} \ N$ where $A$ is a constant and $x$ is the distance from the top of the inclined plane.

If the mass of the block is equal to $2 \ kg$, then what is the energy loss due to frictional force as the block slides down from the top to the bottom?

A weird positional dependent frictional force acts on a block sliding down from the top of an inclined plane of slanting length $10 \ m$ and height $5 \ m$. The dependence of the frictional force on the position is given as $f_r (x)=A \sqrt{x} \ N$ where $A$ is a constant and $x$ is the distance from the top of the inclined plane.

If the velocity of the block at the bottom of the inclined plane is $\sqrt{21} \ m/s$, then what is the value of $A$?

A ball of mass $m$ is used to push down a spring of length $l$ by $x$. The system is then allowed to move from this configuration.

10% of the total mechanical energy of the ball is lost by the time it reaches the topmost point of its trajectory. The height $h$ that the ball rises is equal to:

(Assume the spring constant as $\frac{2mg}{l}$ and the energy transferred to the ball is 100%.)

The potential energy of a 1D system is equal to $U(x)=-x \left(1+ \frac{2}{x} e^{-x} \right)$. Which of the below graphs shows the force $f$ as a function of the position $x$?

A 1D system has a potential energy function, as shown below.

A particle of mass $1.2 \ kg$ is released with zero initial velocity and with an energy of $10 \ J$. Using the graph, determine the velocity of the particle at point $X$.

(Assume the total mechanical energy of the system is a constant.)

A non-constant, non-conservative force $F(t)$ acts on a block, as shown below.

Here, $F(t)=\dfrac{4}{t + 1} \ N$ and $t≥0$.

What is the power delivered to the block as it goes from time $t=2 \ s$ to $t=5 \ s$?

(Hint: Use $P=∫_{t_1}^{t_2} F(t)a(t)dt)$