Work Done by a Variable Force

A spring which is initially in un-stretched condition, is first stretched by a length $x$ and again by a further length $x$. The work done in the first case $W_1$ is one third of the work done in second case $W_2$. True or false?

A woman pushes a trunk on a railway platform which has a rough surface. She supplies a force of $100 \mathrm{N}$ over a distance of $10 \mathrm{m}$. Thereafter, she gets progressively tired and her applied force reduces linearly with distance to $50 \mathrm{N}$. The total distance by which the trunk has been moved is $20 \mathrm{m}$. Calculate the net work done by the two forces over $20 \mathrm{m}$.

A force $F$ acting on an object varies with distance x as shown in the figure. The work done by the force in moving the object from $x=0$ to $x=20 \mathrm{m}$ is

Starting from rest, a particle is moving along x-axis. The variation of force with position is shown in figure. Find the Kinetic energy $\left(KE\right)$ of particle when it is at $x=3\text{m}\text{.}$

Which one of the following physical quantities is represented by the shaded area in the given graph?

The only force acting on a block is along x-axis is given by $\mathrm{F}\mathrm{ }=-\left(\frac{4}{{\mathrm{x}}^2+2}\right)\mathrm{N}$ When the block moves from$\mathrm{x}=-2\mathrm{ }\mathrm{m}$ to $\mathrm{x}=4\mathrm{ }\mathrm{m}$the change in kinetic energy of block is -

If a particle is compelled to move on a given smooth plane curve under the action of given forces in the plane $\overrightarrow{\mathbf{F}}=x\widehat{\mathbf{i}}+y\widehat{\mathbf{j}}$, then

A force $F=A{y}^2+By+C$ acts on a body in the $y$-direction. The work done by this force during a displacement from $y=-a$ to $y=a$ is

A wire of length $L$ suspended vertically from a rigid support is made to suffer extension $l$ in its length by applying a force $F$. The work is

A bullet of mass $10 \mathrm{g}$ is fired horizontally with a velocity $1000 {\mathrm{ms}}^{-1}$ from a rifle situated at a height $50 \mathrm{m}$ above the ground. If the bullet reaches the ground with a velocity $500 {\mathrm{ms}}^{-1}$, the work done against air resistance in the trajectory of the bullet is $(g=10 {\mathrm{ms}}^{-2})$

Graph shows the acceleration of a $3 \mathrm{kg}$ particle as an applied force moves it from rest along $x-$axis. The total work done by the force on the particle by the time the particle reaches $x = 6 \mathrm{m}$, is equal to –

A particle is acted upon by a force F which varies with position x as shown in figure. If the particle at x = 0 has kinetic energy of 25 J, then the kinetic energy of the particle at x = 16 m is

What is the work done by a man in carrying a suitcase weighing $30 \mathrm{kg}$ over his head, when he travels a distance of $10 \mathrm{m}$ in the vertical direction.

The relationship between the force F and position x of a body is as shown in the figure. The work done in displacing the body from x = 1 m to x = 5 m will be: