(D) Given the relation: $t = \sqrt{x} + 3$.Rearranging for $x$: $\sqrt{x} = t - 3$.Squaring both sides: $x = (t - 3)^2$.Velocity $v$ is the derivative

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(D) Given the relation: $t = \sqrt{x} + 3$.Rearranging for $x$: $\sqrt{x} = t - 3$.Squaring both sides: $x = (t - 3)^2$.Velocity $v$ is the derivative of position with respect to time: $v = \frac{dx}{dt} = \frac{d}{dt}(t - 3)^2 = 2(t - 3)$.When the velocity is zero: $2(t - 3) = 0$,which gives $t = 3 \ s$.Initial position at $t = 0 \ s$: $x_i = (0 - 3)^2 = 9 \ m$.Final position at $t = 3 \ s$: $x_f = (3 - 3)^2 = 0 \ m$.Displacement is defined as the change in position: $\Delta x = x_f - x_i = 0 - 9 = -9 \ m$.

Class 11 Physics Motion in Straight Line Uniformly Accelerated Motion

Medium

The relation between the position $x$ and time $t$ of a particle moving in one dimension is given by $t = \sqrt{x} + 3$,where $x$ is in meters and $t$ is in seconds. When the velocity of the particle becomes zero,the displacement of the particle is ........ $m$.

A
$0$
B
$3$
C
$-3$
D
$-9$

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Motion in Straight Line

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Uniformly Accelerated Motion

The position of a particle moving along the $x$-axis is given by $x = (-2t^3 + 3t^2 + 5) \ m$. The acceleration of the particle at the instant its velocity becomes zero is ....... $m/s^2$.

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$A$ particle is moving in a straight line. The variation of position $x$ as a function of time $t$ is given as $x = (t^3 - 6t^2 + 20t + 15) \ m$. The velocity of the body when its acceleration becomes zero is ........... $m/s$.

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$A$ particle moving along the $x-$axis has acceleration $f$ at time $t$,given by $f = f_0(1 - t/T)$,where $f_0$ and $T$ are constants. The particle at $t = 0$ has zero velocity. In the time interval between $t = 0$ and the instant when $f = 0$,the particle's velocity $(v_x)$ is:

DifficultAIPMT 2007

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In some appropriate units,the time $(t)$ and position $(x)$ relation of a moving particle is given by $t = x^2 + x$. The acceleration of the particle is

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The relation between the position $x$ and time $t$ of a particle moving in one dimension is given by $t = \sqrt{x} + 3$,where $x$ is in meters and $t$ is in seconds. When the velocity of the particle becomes zero,the displacement of the particle is ........ $m$.

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The position of a particle moving along the $x$-axis is given by $x = (-2t^3 + 3t^2 + 5) \ m$. The acceleration of the particle at the instant its velocity becomes zero is ....... $m/s^2$.

$A$ particle starting from rest and moving with constant acceleration travels a distance $x$ in the first $2$ seconds and a distance $y$ in the next $2$ seconds. Then:

$A$ particle is moving in a straight line. The variation of position $x$ as a function of time $t$ is given as $x = (t^3 - 6t^2 + 20t + 15) \ m$. The velocity of the body when its acceleration becomes zero is ........... $m/s$.

$A$ particle moving along the $x-$axis has acceleration $f$ at time $t$,given by $f = f_0(1 - t/T)$,where $f_0$ and $T$ are constants. The particle at $t = 0$ has zero velocity. In the time interval between $t = 0$ and the instant when $f = 0$,the particle's velocity $(v_x)$ is:

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