$A$ particle moves along $X-$axis as $x = 4(t - 2) + a(t - 2)^2$. Which of the following is true?

  • A
    The initial velocity of the particle is $4$.
  • B
    The acceleration of the particle is $2a$.
  • C
    The particle is at the origin at $t = 0$.
  • D
    None of these.

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The average velocity of a body moving with uniform acceleration travelling a distance of $3.06 \ m$ is $0.34 \ ms^{-1}$. If the change in velocity of the body is $0.18 \ ms^{-1}$ during this time,its uniform acceleration is ......... $ms^{-2}$.

If the displacement of a particle varies with time as $\sqrt{x} = t + 7$,then

$A$ body moves from rest with a constant acceleration of $5\,m/s^2$. Its instantaneous speed (in $m/s$) at the end of $10\,s$ is:

$A$ particle starts from rest at $x=0 \, m$ with an acceleration of $1 \, m/s^2$. At $t = 5 \, s$,it receives an additional acceleration in the same direction as its motion. At $t = 10 \, s$,its speed and position are $v$ and $x$,respectively. Had the additional acceleration not been provided,its speed and position would have been $v_0$ and $x_0$,respectively. It is found that $x - x_0 = 12.5 \, m$. Then one can conclude that $v - v_0$ is .............. $m/s$.

If average and instantaneous velocities are same,then what is the type of motion?

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