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what is the instantaneous power applied to the particle? if the particle moves with a velocity $(5 \hat{i} - 3 \hat{j} + 6 \hat{k}) {m s}^{- 1}$ under the influence of a constant force $\vec{F} = (10 \hat{i} - 10 \hat{j} + 20 \hat{k}) N.$

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Important Questions on Work, Energy and Power

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A body is moved along a straight line by a machine delivering constant power. The distance moved by the body in time '

t

' is proportional to

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A particle is moving unidirectional on a horizontal plane under the action of a constant power supplying energy source. The displacement (s) – time (t) graph that describes the motion of the particle is (graphs are drawn schematically and are not to scale):

EASY

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A body is initially at rest. It undergoes one dimensional motion with constant acceleration. The power delivered to it at time

t

is proportional to

EASY

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A body of mass

m

accelerates uniformly from rest to

v_{1}

in the time

t_{1}

. The instantaneous power delivered to the body as a function of time

EASY

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The heart of a man pumps

5

litres of blood through the arteries per minute at a pressure of

150 mm

of mercury. If the density of mercury be

13.6 \times 10^{3} k g m^{- 3}

and

g = 10 m s^{- 2}

, then the power of heart in watt is:

HARD

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A body starts from rest, under the action of an engine working at constant power and moves along a straight line. The displacement $s$ is given as a function of time $t$ as:

EASY

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A body of mass

2 kg

is driven by an engine delivering a constant power of

1 J s^{- 1}

. the body starts from rest and moves in a straight line. After

9 s

, the body has moved a distance (in

m

)….

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Water is pumped steadily out of a flooded basement, at the speed of

10 m s^{- 1}

through a hose (tube) of radius,

1 cm,

passing through a window,

3 m

above the water level. The power of the pump is (Assume

g = 10 m s^{- 2}

, density of water

= 1000 kg m^{- 3}

)

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Water falls down a

500.0 m

shaft to reach a turbine which generates electricity. How much water must fall per second in order to generate

1.00 \times 10^{9}

watts of power ? (Assume

50 %

efficiency of conversion and

g = 10 m s^{- 1}

)

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A car of weight W is on an inclined road that rises by 100 m over a distance of 1km and applies a constant frictional force

\frac{W}{20}

on the car. While moving uphill on the road at a speed of

10 m s^{- 1}

, the car needs power P. If it needs power

\frac{P}{2}

while moving downhill at speed

υ

then value of

υ

is:

EASY

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A constant power delivering machine has towed a box, which was initially at rest, along a horizontal straight line. The distance moved by the box in time

t

is proportional to :-

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In each heartbeat, a heart pumps

80 m l

of blood at an average pressure of

100 mm

Hg

. Assuming

60

heartbeats per second, the power output of the heart is

(ρ_{H g} = 13.6 \times 10^{3} k g m^{- 3}) (g = 9.8 m s^{- 2})

EASY

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

HARD

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A car of mass

m

accelerates on a level smooth road when a constant power

p

is delivered to it. If the velocity of the car at any instant is

v,

then its velocity will be doubled after travelling a distance

HARD

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An automobile of mass

m

accelerates starting from the origin and initially at rest, while the engine supplies constant power

P

. The position is given as a function of time by:

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Water is falling on the blades of a turbine from a height of

25 m . 3 \times 10^{3} kg

of water pours on the blade per minute. If the whole of energy is transferred to the turbine, power delivered is:

EASY

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An engine develops

20 kW

of power. How much time will it take to lift a mass of

200 kg

to a height of

40 m ? (g = 10 m s^{- 2})

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A particle of mass M is moving in a circle of fixed radius R in such a way that its centripetal acceleration at time t is given by

n^{2} R t^{2}

, where

n

is a constant. The power delivered to the particle by the force acting on it, is :

EASY

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A body of mass

1 kg

begins to move from rest under the action of a time dependent force

\vec{F} = (2 t \hat{i} + 3 t^{2} \hat{j}) N

, where

\hat{i}

and

\hat{j}

are unit vectors along x and y axis. What power will be developed by the force at the time t?

MEDIUM

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A particle of mass

m

is driven by a machine that delivers a constant power

k

watts. If the particle starts from rest the force on the particle at time

t

is:

what is the instantaneous power applied to the particle? if the particle moves with a velocity 5i^-3j^+6k^m s-1 under the influence of a constant force F⁡→=10i⁡^-10j⁡^+20k^N.

Important Questions on Work, Energy and Power

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what is the instantaneous power applied to the particle? if the particle moves with a velocity $(5 \hat{i} - 3 \hat{j} + 6 \hat{k}) {m s}^{- 1}$ under the influence of a constant force $\vec{F} = (10 \hat{i} - 10 \hat{j} + 20 \hat{k}) N.$