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v^2-u^2=2ah

v=u/4
a=-g
u^2(1/16 - 1)=-2*10*h
h=3/64 u^2

when battery is short circuited, its internal resistance is zero. hence v=E

Let time taken by boy be t.

the distance travelled by boy is d=10t

distance covered by train in this time is d-48

for train
d-48=1/2 a t^2
10t-48=1/2t^2
t^2-20t+96=0
(t-12)(t-8)=0

t=12 or t=8

So minimum time t is 8 secs.

rate me if you find my answer useful

h=ut-1/2 gt^ (minus sign because velocity is upwards and acceleration is downwards)

gt^-2ut+2h=0

These gives two values of t and the difference between them is @t

(@t)^=(t1+t2)^-4*t1* t2

(@t)^=4*u^/g^-4*2h/g

This gives u=1/2 & 8hg+g^(@t)^

So answer is c

For maths ML Khanna is best according to me.
For physics HC Verma
Chemstry-morrison n boyd, jd lee and p bahadur

Snail is right. The word always should have been there in the question.

Let us consider some cases.
1) A particle moves around a circle with constant magnitude of velocity. Here, direction of velocity is changing but magnitude is not. Then on completing the circle, average velocity is 0 but average speed is not. Similarly displacement is 0 but distance is not.

2) A particle is moving in a straight line in the same direction but the magnitude of velocity is constantly changing. Hence velocity is variable. Then, average velocity and average speed will be same and so will be the distance and displacement.

Thus when velocity is variable average speed and average velocity may or may not be the same. The same holds for distance and displacement.

Instantaneous speed and instantaneous velocity are always equal as the time tends to 0 and hence distance and displacement can be approximated to be the same. And we know that
instantaneous speed=distance/t
instantaneous velocity=displacement/t
As t tends to zero, distance=displacement and hence the result.

height reached by stone is
h=u^2/2g=1.25m
time taken is
t=u/a=0.5s

Time taken to come to base t1=4-0.5=3.5s
total distance covered s=1/2g*(t1)^2=61.25m

So, height of cliff=61.25-1.25=60m

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Ans is 1.5 i.e. (A)

go through the formulas and solved examples from some standard book and then try to solve the problems yourself...

Its probably given in vector notation

There's no harm in giving it a shot.
I feel that it is worth losing a year if you are satisfied at the end.

I am also in a similar situation.
At present I am studying Electronics in Jadavpur University in Kolkata which is considered to be the best stream of a college which is among the top colleges in India.
But it is my aim to study in an IIT. In this years JEE I got a very low rank and therefore I am going for IIT-JEE again next year. And I dont mind even if I have to drop a year.

Ans 3:
Let spring be stretched by x;
kx=mg-m/d1*d2g
kx=12-2
or x=1/20
PE of spring=1/2k*x^2=1/2*200*1/400=1/4
After breaking the block will come to the bottom. So its PE will also be converted to heat
PE of block=1.2*10*.4=4.8

Rise in temo of water and block will be same say dT
m1d1 dT+m2d2 dT=5.05
dT=3.63*10^-3

Ans 2:
Change in KE=mg(h1-h2)=5m
Now 40/100*5m=m*800*dT
or dT=2.5*10^-3