A particle starts moving from position of rest under a constant acceleration. If it travels a distance x in t second, what distance will it travel in next t second? 


Given, 

Initial velocity, u = 0

Distance travelled, s = x

Time taken to travel x distance, t = t sec

Now, using the relation, 

straight s space equals space ut plus space 1 half at squared comma we have
x = 0 + 1/2 at2                     ... (1)

Let the body travel a distance y in next t seconds. 

The total distance travelled in t+t = 2t sec will be (x+y).

Therefore, 

(x+y) = 1/2 a (2t)2

          = 1/2a x 4t2                 ... (2)

Dividing equation (2) by (1), we have

space space space space space space fraction numerator left parenthesis straight x plus straight y right parenthesis over denominator straight x end fraction space equals space 4 space

rightwards double arrow space space space space space space space space space space space straight y space equals space 3 straight x
 

 
  




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A train 100 m long is moving with a velocity of 60 km/hr. Find the time it takes to cross the bridge 1 km long. 

Total distance to be travelled, s = 100 + 1000 = 1100 m 


Velocity, v = 60 km/hr = 50/3 m/s 

Therefore, 

Time taken to cross the bridge, t = straight s over straight v space equals space fraction numerator 1100 over denominator bevelled 50 over 3 end fraction space equals space 66 space sec 


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Is it necessary to aim a little above the target hit at ? Explain.


Yes, for example if you are throwing a dart at the board, position the dart a little above the target in order to hit the target. This will enable you to hit the target accurately as the dart will follow a projectile motion. 

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A heavy and a light body are dropped from the top of a tower simultaneously. Which will reach the ground first?

During the vertical fall of a body, the time taken for the body to fall is given by, 

                     straight t space equals space square root of fraction numerator 2 straight h over denominator straight g end fraction end root ,

which is independent of the mass of the body. 

Hence, both the bodies will reach the ground simultaneously. 

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The K.E of a particle moving along a circle of radius r depends upon the distance covered s as, K = as2. What is the force acting on the particle? 


Given, 

K.E, K = 1/2 mv2 

This implies, 

mv2 = 2K 

When the body is moving in a circle, 


straight F space equals space mv squared over straight r space equals space fraction numerator 2 straight K over denominator straight r end fraction space equals space fraction numerator 2 as squared over denominator straight r end fraction, is the required force. 

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