assignment - 3

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Straight Line Motion

• Two trains A & B of length 300m each are moving on two parallel tracks with a uniform speed of 54 km/hr in the same direction, with A ahead of B. The driver of A decides to overtake A and accelerates by 2 m/s/s. If after 25 seconds , the guard of B just brushes past the driver of A, what was the original distance between them?                                                                             [25 m ]
• A car accelerates from rest at a constant rate A for some time after which it retards at constant rate B to come to rest.If the time elapsed is T seconds, calculate the maximum velocity reached and the total distance travelled in terms of A,B & T.
• Drops of water from the roof of a house 6 m high falls at a regular intervals . The first drop reaches the ground at an instant of time when third drop leaves the roof. Find the height of the second drop at that instant.                                                                                                             [ 4.5 m, from the ground ] 
• A metal ball is allowed to fall freely on a perfectly elastic plane from a height of 3m. At  t  = 0 , the speed of the ball is zero. Represent graphically the variation of velocity with time.
• A ball is thrown vertically upward . After some time it returns back to earth . Draw speed time graph for the ball.
• A ball is thrown vertically upward with a velocity of 20 m/s. It takes 4 s to return to its original position.Draw velocity time graph for the ball.
• Can an object be accelerated without speeding up or slowing down? Explain.
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conceptual questions

1. Can a quantity have units but still be dimensionless?
2. Can a quantity have dimensions but still be unit less?
3. Name two physical quantities which have same dimensions as that of work?
4. Name two physical quantities which have same dimensions as that of pressure?
5. State the number of significant figures in the following :

           (a) 0.0074    (b) 0.23700     (c) 6.230    (d) 89000  (e) 1.0102
     
     6.  Solve the following with due regard to significant figures :
          (a)   .996 x 3.52                     (b) 7.21/2.3

     7.  The diameter of a circle is 2.486 m. Calculate its area with
          due regard to significant figures .
     8.  Bring out the difference between 4.0 and 4.000.
     9.  The length and breadth of a rectangular field are 22.4 cm
           and 15.8 cm respectively and have been measured to an
          accuracy of 0.2 cm. F ind the % error in the measurement
          of its area.