A body of mass 0.5 kg is supplied with a power ' $P$ ' (in watt) which varies with time ' $f$ ' (in second) as $P=3 t^2+3$. If the velocity of the body at time $t=0$ is zero, then the velocity of the body at time $t=3 \mathrm{~s}$ is

The work done in displacing a particle from $y=a$ to $y=2 a$ by a force $-\frac{K}{y^2}$ acting along $Y$-axis is

A body of mass 500 g is falling from rest from a height of 3.2 m from the ground. If the body reaches the ground with a velocity of $6 \mathrm{~ms}^{-1}$, then the energy lost by the body due to air resistance is (Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

An engine is dragging a mass of 5000 kg with a velocity of $5 \mathrm{~ms}^{-1}$ along a smooth inclined plane of inclination 1 in 50 . Then the power of the engine is

A body is moved along a straight line by an engine which delivers a constant power. The distance moved by the body in time $t$ is proportional to

A body of mass 3 kg is moving under the action of a force which causes a displacement of $\left(t^3 / 3\right) \mathrm{m}$, where $t$ is time in seconds. The work done by the force in first 2 sec is

While a person climbs stairs, the gravitational potential energy of the person increases. The source of this energy is

A boat of mass 1000 kg goes from rest to speed 20.0 $\mathrm{m} / \mathrm{s}$ in 5.0 s . The water exerts a constant drag force and the acceleration of the boat is constant. If the average power required by the boat is 45000 W , then the magnitude of the drag force is

A pump on the ground floor of a building can pump up water to fill a tank of volume $36 \mathrm{~m}^3$ in 30 min . If the tank is 50 m above the ground, and the electric power consumed by the pump is 40 k W , the efficiency of the pump is

(use $g=10 \mathrm{~m} / \mathrm{s}^2$ and density of water $=1000 \mathrm{~kg} / \mathrm{m}^3$ )

Statement I The slope of kinetic energy-displacement curve of a body in motion will be directly proportional to its acceleration.

Statement II From a height of 15 m , a ball is projected vertically upwards with a velocity of $30 \mathrm{~m} / \mathrm{s}$. If the ball rises to the same height after hitting the ground, the loss of its energy on hitting the ground is $30 \%$.

Statement III The velocity acquired by a body of mass $m$ after travelling a fixed distance from rest under the action of a constant force is directly proportional to mass $m$.

Which of the following is correct?

An object is moving in a straight line under the influence of a source of constant power. If $v$ and $t$ are velocity and time respectively, then

A ball of mass 1 kg moves in a straight line with velocity $v=c x^\alpha$, where $c=1$ (SI unit) and $\alpha$ is a constant. If the work done by the net force during its displacement from $x=0$ to $x=4 \mathrm{~m}$ is 128 J , then the $\alpha$ is

The potential energy of an object is $U(x)=\left(5 x^2-4 x^3\right) \mathrm{J}$, where $x$ is the position in metre. The position at which the force becomes zero is

The block starts from rest as shown in the figure. Find the work done by force of 10 N and friction in the time 0 to 4 s . [Take, $g=10 \mathrm{~m} / \mathrm{s}^2$ ]

Under action of force, a 2 kg body moves such that its position $x$ as function of time $t$ is given by $x=\alpha t^2 / 2$, where $x$ is in metre, $t$ is in seconds and $\alpha=1 \mathrm{~m} / \mathrm{s}^2$. The work done by the force in the first two seconds is

Identify the incorrect statement.

A force acts on a 30 g particle in such a way that the position of the particle as a function of time is given by $x=\alpha t^2$, where $x$ is in metre, $t$ is in seconds and $\alpha=1 \mathrm{m} / \mathrm{s}^2$. The work done during the first 4 s is

A force $\mathbf{F}=(2 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}) \mathrm{N}$ is applied on an object of mass $M$. What is the work done by this force in moving the object horizontally along the $X$-axis by 3 m ?

A ball of mass $m=1 \mathrm{~kg}$ is thrown from the top of a building with initial velocity $\mathbf{v}=(20 \mathrm{~m} / \mathrm{s}) \hat{\mathbf{i}}+(24 \mathrm{~m} / \mathrm{s}) \hat{\mathbf{j}}$ at time $t=0$. The change in the potential energy of the ball between $t=0$ and $t=6 \mathrm{~s}$, if the ball does not hit the ground, then (assume, $g=10 \mathrm{~m} \mathrm{~s}^2$ )

When a body is acted upon by a resultant force, then the work done by the resultant force is equal to

A force acts on a body of mass 10 kg , resulting in its displacement given as $x=\left(\frac{t^3}{25}\right) \mathrm{m}$, where $t$ is the time in seconds. The work done by the force in 5 s is