Mechanical Power

A car of mass $1.0\times {10}^3 \mathrm{kg}$, starts from rest and maintains an acceleration of $5.0 \mathrm{m} {\mathrm{s}}^{-2}$ for $6.0 \mathrm{s}$ in the $+x$ direction as shown in the figure. Assume that a single horizontal force (not shown) accelerates the car. Determine the average power generated by this force.

An automobile of mass $m$ accelerates, starting from rest, while the engine supplies constant power $P$. Find its position and instantaneous velocity changes with respect to time.

A car of mass $500 \mathrm{kg}$ moving with a speed $36 \mathrm{km} {\mathrm{h}}^{-1}$ in a straight road unidirectionally doubles its speed in $1 \min$. Find the power delivered by the engine.

A small body of mass $m$ is located on a horizontal plane at the point $O$. The body acquires a horizontal velocity $v_{\mathrm{o}}$. Find the mean power developed by the friction force during the whole time of motion, if the frictional coefficient $\mu =0.27$, $m=1.0 \mathrm{kg}$ and $v_{\mathrm{o}}=1.5{ \mathrm{m} \mathrm{s}}^{-1}$.

A horizontal constant force $F$ pulls a block of mass $m$ placed on a horizontal surface. If the coefficient of kinetic friction between the block and ground is $\mu$, find the power delivered by the external agent after a time $t$ measured from the beginning of action of the force.

A body is thrown with a velocity $v_0$ at an angle ${\mathrm{\theta }}_0$ with horizontal. Find the $\left(\mathrm{a}\right)$ instantaneous power delivered by gravity after a time $t$ measured from the instant of projection and $\left(\mathrm{b}\right)$ average power delivered by gravity during the time $t$.

An elevator of mass $M$ with a person of mass $m$ is moving upward with uniform velocity $\overrightarrow{v}$. What is the power delivered by the elevator?

An insect of mass $m$ moves up along a hanging stationary thread, with acceleration $a$. Find the power delivered by gravity after a time $t$.

Consider a machine that delivers power to a body, that is proportional to the velocity of the body. If the body starts with a velocity that is almost negligible, then the distance covered by the body is proportional to

A particle $A$ of mass $\frac{10}{7} \mathrm{kg}$ is moving in the positive direction of $x-$axis. At initial position $x=0$, its velocity is $1 \mathrm{m} {\mathrm{s}}^{-1}$, then its velocity at $x=10 \mathrm{m}$ is (use the graph given)

A block of mass $m$ is being pulled up a rough incline by an agent delivering constant power $P$. The coefficient of friction between the block and the incline is $\mu$. The maximum speed of the block during the course of ascent is

A particle of mass $m$ is projected at an angle $\alpha$ to the horizontal with an initial velocity $u$. The average power delivered by gravity during the time it reaches its highest point is

A car drives along a straight level frictionless road by an engine delivering constant power. Then velocity is directly proportional to 

A body is moved along a straight line by a machine delivering a constant power. The distance moved by the body in time $t$ is proportional to 

The speed $v$ reached by a car of mass $m$ in travelling a distance $x$, driven with constant power $P$, is given by

A particle of mass $m$ is moving in a circular path of constant radius $r$, such that its centripetal force $F_r$ varies with time $t$ as $F_r= k^{2}r{t}^2$, where $k$ is a constant. What is the power delivered to the particle by the forces acting on it?

Water falling from a $50 \mathrm{m}$ high fall is to be used for generating electric energy. If $1.8\times {10}^5 \mathrm{kg}$ of water falls per hour and half the gravitational potential energy can be converted into electric energy, how many $100 \mathrm{W}$ lamps can be lit?

The electric motor of a model train accelerates the train from rest to $0.620 \mathrm{m} {\mathrm{s}}^{-1}$ in $21.0 \mathrm{ms}$. The total mass of the train is $875 \mathrm{g}$. Find the average power delivered to the train during the acceleration.

A $700 \mathrm{N}$ marine in basic training climbs a $10.0 \mathrm{m}$ vertical rope at a constant speed in $8.00 \mathrm{s}$. What is his power output?

A helicopter lifts a body of mass $100 \mathrm{kg}$ to a height of $500 \mathrm{m}$ at a constant speed. It takes $5 \min$ to lift the body. Find the work done by the helicopter and the power required.