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    Motion in A Plane
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    A particle moves in a plane with constant acceleration in direction different from initial velocity. Can ever the particle have velocity parallel to acceleration? Explain your answer. 

    A component of initial velocity is in a perpendicular direction to the direction of acceleration. It is given that acceleration remains constant and cannot be reduced to zero. 
    Velocity will be parallel to acceleration if and only if, component of velocity perpendicular to acceleration is zero. 
    Therefore the particle moving in a plane with constant acceleration in direction different from initial velocity can never have velocity parallel to acceleration.
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    A particle has arbitrary motion in the space. Which of the following statements are true or false?
    (i)  Total length of path is always equal to magnitude of displacement of particle.
    (ii)  Average speed is always less than instantaneous speed.
    (iii) Position of particle at any instant is given by straight r with rightwards arrow on top equals stack straight r subscript 0 with rightwards arrow on top plus straight u with rightwards arrow on top straight t plus 1 half straight a with rightwards arrow on top straight t squared.
    (iv) Average acceleration of motion is zero if initial and Final velocity of a particle is same.

    (i) False, the total length of path is either greater or equal to magnitude of displacement. This statement is true only if the particle is moving in a straight path.

    (ii) False, average speed may be less, equal or greater than the speed at any instant.

    (iii) False, the given relation is true only for uniform accelerated motion.

    (iv)True. For a particle moving with a constant velocity, acceleration will remain the same. 

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    A boy sitting in a train moving with constant velocity throws a ball straight up into air. Will the ball fall behind him?
    The ball is thrown in vertically upward direction and given that the train is moving up with a constant velocity. therefore, the horizontal velocity of the train and ball are both same. And, the ball travels the same horizontal distance as that of the train. 

    Therefore, the ball will come back into the hands of thrower. 
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    Answer
    A truck travelling due north at 20 m/s turns left and travels at same speed. Find the change in velocity.

    Let unit vector along north is straight i with hat on top and that along west is straight j with hat on top. Thus,
                  stack straight v subscript 1 with rightwards arrow on top space equals space 20 space straight i with hat on top

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    Let unit vector along north is  and that along west is  Thus,  ?
    Now the change in velocity of truck is,
             increment straight v with rightwards arrow on top equals stack straight v subscript 2 with rightwards arrow on top minus stack straight v subscript 1 with rightwards arrow on top equals 20 straight j with hat on top minus 20 straight i with hat on top
                    equals 20 square root of 2 space due space SW

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    Answer

    The position of particle at any instant is given by straight r with rightwards arrow on top equals 2 straight t squared straight i with hat on top plus 4 straight t straight j with hat on top. What is the displacement of particle in first 3 seconds?

    Given,

    Position of particle at any instant,
    ∴

    Initial displacement of the particle is,    

    and

    Displacement of particle when t =3 sec is,
         

    Displacement of particle in first three sec. is,

                       

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