Work-energy theorem

Velocity-time graph for a body of mass 10 kg is shown in figure. Work-done on the body in first two seconds of the motion is :

Consider an elliptically shaped rail PQ in the vertical plane with OP = 3 m and OQ = 4 m. A block of mass 1 kg is pulled along the rail from P to Q with a force of 18 N, which is always parallel to line PQ (see the figure given). Assuming no frictional losses, the kinetic energy of the block when it reaches Q is $(n\times10)$ Joules. The value of $n$ is (take acceleration due to gravity $=10\ \mathrm{m\,s^{-2}}$)

A small ball of mass m starts at a point A with speed $v_o$ and moves along a frictionless track AB as shown. The track BC has coefficient of friction $\mu$. The ball comes to stop at C after travelling a distance L which is :

The average mass of rain drops is $3.0\times10^{-5}$ kg and their average terminal velocity is 9 m/s. Calculate the energy transferred by rain to each square metre of the surface at a place which receives 100 cm of rain in a year.

A spring of unstretched length $l$ has a mass m with one end fixed to a rigid support. Assuming spring to be made of a uniform wire, the kinetic energy possessed by it if its free end is pulled with uniform velocity $v$ is :

A bullet looses $\left(\dfrac1n\right)^{\text{th}}$ of its velocity passing through one plank. The number of such planks that are required to stop the bullet can be :

A particle of mass 0.2 kg is moving in one dimension under a force that delivers a constant power 0.5 W to the particle. If the initial speed (in m s$^{-1}$) of the particle is zero, the speed (in m s$^{-1}$) after 5 s is

The speed of the block when it reaches the point $Q$ is

A block of mass 2 kg is free to move along the $x$-axis. It is at rest and from $t=0$ onwards it is subjected to a time-dependent force $F(t)$ in the $x$ direction. The force $F(t)$ varies with $t$ as shown in the figure. The kinetic energy of the block after 4.5 seconds is

STATEMENT-1: A block of mass $m$ starts moving on a rough horizontal surface with a velocity $v$. It stops due to friction between the block and the surface after moving through a certain distance. The surface is now tilted to an angle of 30° with the horizontal and the same block is made to go up on the surface with the same initial velocity $v$. The decrease in the mechanical energy in the second situation is smaller than that in the first situation.

because

STATEMENT-2: The coefficient of friction between the block and the surface decreases with the increase in the angle of inclination.