Acceleration and Avg acceleration questions with solutions

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• NumericmediumKinematics Part-1 (one dimension)Acceleration and Avg acceleration

  The distance x covered by a particle in one-dimensional motion varies with time as x²=at²+2bt+c. If its acceleration depends on x as x⁻ⁿ, where n is an integer, find n.

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• MCQmediumKinematics Part-1 (one dimension)Acceleration and Avg acceleration

  A particle starts with speed u and obeys a = -kv². The distance travelled before its speed becomes u/2 is:

  Options

  • Option A

    1/(2k)

  • Option B

    ln2/k

  • Option C

    1/k

  • Option D

    2ln2/k

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• MCQmediumKinematics Part-1 (one dimension)Acceleration and Avg acceleration

  A particle of unit mass undergoes one-dimensional motion such that its velocity varies according to v(x) = βx⁻²ⁿ, where β and n are constants and x is the position of the particle. The acceleration of the particle as a function of x is:

  Options

  • Option A

    -2nβ²x⁻²ⁿ⁻¹

  • Option B

    -2nβ²x⁻⁴ⁿ⁻¹

  • Option C

    -2nβ²x⁻²ⁿ⁺¹

  • Option D

    -2nβ²x⁻⁴ⁿ⁺¹

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• MCQmediumKinematics Part-1 (one dimension)Acceleration and Avg acceleration

  A particle moves along the x-axis and has its displacement x varying with time t according to the equation:

  $x=c_0\left(t^2-2\right)+c\left(t-2\right)^2$

  where and $c_0$ are constants of appropriate dimensions.

  Then, which of the following statements is correct?

  Options

  • Option A

    the acceleration of the particle is 2(c+$c_0$)
    

  • Option B

    the acceleration of the particle is 2$c_0$

  • Option C

    the acceleration of the particle is 2c

  • Option D

    the initial velocity of the particle is 4c

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• MCQeasyKinematics Part-1 (one dimension)Acceleration and Avg acceleration

  A particle has v(0)=1 m s⁻¹ and a = 12t² - 6t. At the non-zero instant at which acceleration vanishes, its velocity is:

  Options

  • Option A

    1/2 m s⁻¹

  • Option B

    $\frac{3}{4}$ m s⁻¹

  • Option C

    1 m s⁻¹

  • Option D

    5/4 m s⁻¹

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• MCQmediumKinematics Part-1 (one dimension)Acceleration and Avg acceleration

  The position vector of a particle is r(t)=15t²î+(4-20t²)ĵ. What is the magnitude of acceleration at t=1?

  Options

  • Option A

    40

  • Option B

    100

  • Option C

    25

  • Option D

    50

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• Multi-correctdifficultKinematics Part-1 (one dimension)Acceleration and Avg acceleration

  The displacement of a particle depends on time as x=αt²-βt³. Which statements are correct?

  Select all that apply

  • Option A

    The particle returns to its starting point after time α/β.

  • Option B

    The particle comes to rest after time 2α/(3β).

  • Option C

    The initial velocity is zero but initial acceleration is non-zero.

  • Option D

    No net force acts on the particle at time α/(3β).

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• MCQeasyKinematics Part-1 (one dimension)Acceleration and Avg acceleration

  A particle moves along the x-axis and its displacement varies with time as x = c₀(t²-2) + c(t-2)², where c₀ and c are constants of appropriate dimensions. Which statement is correct?

  Options

  • Option A

    The initial velocity of the particle is 4c

  • Option B

    The acceleration of the particle is 2(c+c₀)

  • Option C

    The acceleration of the particle is 2c

  • Option D

    The acceleration of the particle is 2c₀

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• MCQmediumKinematics Part-1 (one dimension)Acceleration and Avg acceleration

  A car moves eastward at 20 m s⁻¹ and takes a left turn in 5 s without changing speed. Find its average acceleration during the 5 s.

  

  Options

  • Option A

    4√2 m s⁻² towards NE

  • Option B

    4√2 m s⁻² towards NW

  • Option C

    4 m s⁻² towards NE

  • Option D

    Zero

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• Multi-correctmediumKinematics Part-1 (one dimension)Acceleration and Avg acceleration

  A particle starts with velocity u>0 and obeys a=-kv. Which statements are correct?

  Select all that apply

  • Option A

    v=ue⁻ᵏᵗ

  • Option B

    v=u-kx

  • Option C

    Total distance travelled as t→∞ is u/k.

  • Option D

    The particle comes exactly to rest after a finite time.

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