Moumita D.

A conservative force is a force with the property that the work done in moving a particle between two points is independent of the taken path. A conservative force is dependent only on the position of the object.

To put it another way, the work done depends only on the initial and final position of the particle.

Suppose we throw a object of mass ‘m’ upward suppose it goes up to a height h.

then the work done in throwing object in upward direction w1 = -mgh (use ‘-g’ sign convention )

and the work done while returning to the same path w2 = mgh

total work done W = w1 + w2 = -mgh+mgh = 0

Hence, total energy loss will also be zero in this case.Hence the total workdone in travelling a certain height and falling back to tha same place is zero. This is the property of coservative force as the total workdone depends only on the initial and final positions of the objects. So, Gravitational Force is Conservative Force.

Assuming the pond has vertical banks and a non-porous bottom and sides (so we need not worry about drainage and such) then the pond level will be increased when we put the boat in the water . A heavier boat will displace more water. When we remove the rock from the boat the boat will displace less water and the pond  level will decrease.

Newton’s Law of Cooling states that the rate of change of temperature of a body is proportional to the difference between the temperature of the body and that of the surrounding medium. It is a reasonably accurate approximation in some circumstances.

More precisely, let T denote the temperature of an object and Tο the ambient temperature.   if t denotes time, then Newton's law states that

dT/dt  = -k(T-Tο)

where k is a positive constant. Thus, if the object temperature is much higher than its surroundings, then  T-Tο is large and positive, so dTdT/dt is large and negative, so the object cools quickly. If the object temperature is only slightly higher than its surroundings, then T-Tο is small positive, and the object cools slowly. So a cup of coffee will cool more quickly if you put it in the refrigerator! 

Newton’s Law of Cooling states that the rate of temperature of the body is proportional to the difference between the temperature of the body and that of the surrounding medium. It is a reasonably accurate approximation in some circumstances.

More precisely, let T denote the temperature of an object and Tο the ambient temperature.   if t denotes time, then Newton's law states that

dT/dt  = -k(T-Tο)

where k is a positive constant. Thus, if the object temperature is much higher than its surroundings, then  T-Tο is large and positive, so dTdT/dt is large and negative, so the object cools quickly. If the object temperature is only slightly higher than its surroundings, then T-Tο is small positive, and the object cools slowly. So a cup of coffee will cool more quickly if you put it in the refrigerator! 

mass=1000kg 
u=0km/hr=0m/s 
v=54km/hr=15m/s 
work= change in kinetic energy 
= 1/2xmxv^2 - 1/2xmxu^2 
= 1/2x1000x15^2 - 0 
=112500 J 
power = work/time 
= 112500/5 = 22500 J/s=22.5 kw

from first eqution of motion

v=u+at

u=0

therfore

v=at

15=5a

a=3m/s^2

from second equation of motion 

s=ut+/2at^2

0+1/2*3*5*%

s=37.5 m

now v avg=dsance/time=37.5/5=7.5 m/s

gaain in KE=KE fina=KE initial

=1/2mv^2-1/2mv2^2

=1/2*1000*15^=112.5kj