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Motion Test - 21

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Motion Test - 21
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  • Question 1
    1 / -0
    From kinematics, correct equation of motion for $$S$$ is/are :
    Solution
    According to the second equation of motion,

    $$s = ut+\dfrac{1}{2}at^2$$

    where, $$s$$=displacement
    $$u$$=initial velocity
    $$t$$ = time
    $$a$$=acceleration

    (i) If the displacement and acceleration are in the same direction, then,

    $$s=ut+\dfrac{1}{2}at^2$$
    where $$a$$ is the magnitude of the acceleration

    For example, a car linearly accelerating on road.

    (ii) If the displacement and acceleration are in the opposite direction, then,

    $$s=ut-\dfrac{1}{2}at^2$$
    where $$a$$ is the magnitude of the acceleration

    For example, a ball thrown vertically upwards in air

    Hence, the correct option is C. 
  • Question 2
    1 / -0
    Is it possible to have an accelerated motion with a constant speed? Name such type of motion.
    Solution
    Yes it is possible. Let us take an example, circular motion. In this it has acceleration because direction of motion is changing but it has constant speed  along tangential. Hence it is possible.
  • Question 3
    1 / -0
    Which of the following quantity remains constant in a uniform circular motion?
    Solution
    In a uniform circular motion, the direction of velocity changes but its magnitude remains constant, hence, speed remains constant in a uniform circular motion.
    Hence the correct answer is B
  • Question 4
    1 / -0
    The distance $$x$$ covered in time $$t$$ by a body having initial velocity $${ v }_{ 0 }$$ and having constant acceleration $$a$$ is given by $$x={ v }_{ 0 }t+1/2a{ t }^{ 2 }$$. This result follows from :
    Solution
    The given equation is the fundamental equation of kinematics. So it can not follow from any Newton's law of motion.
    Ans:(D)
  • Question 5
    1 / -0
    A food packet is released from a helicopter rising steadily at the speed of $$2\ { m }/{ s }$$. After $$2$$ seconds the velocity of the packet is (Take $$g=10  { m }/{ { s }^{ 2 } } $$):
    Solution
    The food packet has an initial velocity $$u= 2\ { m }/{ s }$$ in upward direction, 
    $$g= 10 \ m/s^2$$
    $$t= 2 \ s$$

    Using the first equation of motion, $$v = u+at$$

    Taking the upward direction as negative and downward direction as positive

    $$v=-2+10\times 2=18\  { m }/{ s }$$

    Hence, the velocity of the packet is $$18 \ m/s$$ in the downward direction.
  • Question 6
    1 / -0
    Which of the following is/are true about retardation
    Solution
    Retardation is opposite of acceleration. In case of acceleration, velocity increases with time and in case of retardation, velocity decreases over time.
  • Question 7
    1 / -0
    For a body moving with an initial velocity $$u$$ and uniform acceleration $$a$$. Find the displacement of the body in time t.
    Solution
    From the second equation of motion, if u = initial velocity , a= acceleration and t= time then
    $$s=ut+\dfrac{1}{2}at^2$$
  • Question 8
    1 / -0
    Which of the following is true about distance and time.
    Solution
    $$ Speed = \dfrac{Distance}{Time} $$

    For uniform velocity, Distance $$\propto$$ Time
  • Question 9
    1 / -0
    A body starts from rest and acquires a velocity $$10m s^{-1}$$  in 2 s. Find the acceleration.
    Solution
    Acceleration = Change in velocity per unit time.

    Therefore, Acceleration $$a = \dfrac{10 m/s}{2 s} = 5 m/s^2 $$
  • Question 10
    1 / -0
    A car starting from rest acquires a velocity $$180\ m s^{-1}$$ in 0.05 h. Find the acceleration.
    Solution
    Acceleration, $$a = \dfrac{180 m/s}{0.05\times 3600 s} = 1 m/s^2 $$
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