(D) The velocity is given by $v = x^2 + x$.Acceleration $a$ is defined as $a = \frac{dv}{dt}$.Using the chain rule,$a = \frac{dv}{dx} \cdot \frac{dx}{

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(D) The velocity is given by $v = x^2 + x$.Acceleration $a$ is defined as $a = \frac{dv}{dt}$.Using the chain rule,$a = \frac{dv}{dx} \cdot \frac{dx}{dt} = v \frac{dv}{dx}$.Differentiating $v$ with respect to $x$: $\frac{dv}{dx} = \frac{d}{dx}(x^2 + x) = 2x + 1$.Substituting $v$ and $\frac{dv}{dx}$ into the acceleration formula: $a = (x^2 + x)(2x + 1)$.At $x = 2 \ m$:$a = (2^2 + 2)(2(2) + 1) = (4 + 2)(4 + 1) = 6 \times 5 = 30 \ m/s^2$.

Class 11 Physics Motion in Straight Line Instantaneous Velocity and Speed and Velocity-time Graph

Medium

The velocity of a particle moving on the $x$-axis is given by $v = x^2 + x$,where $v$ is in $m/s$ and $x$ is in $m$. Find its acceleration in $m/s^2$ when passing through the point $x = 2 \ m$.

A
$0$
B
$5$
C
$11$
D
$30$

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Motion in Straight Line

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Instantaneous Velocity and Speed and Velocity-time Graph

The graph shows the variation with time $t$ of velocity $v$ of an object moving along a straight line. The $a-t$ graph will be:

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The speed-time graph of a particle moving along a fixed direction is shown in the figure. Obtain the distance (in $m$) traversed by the particle between $t=0\; s$ and $t=10\; s$.

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The position-time graph of a particle moving along a straight line is shown,which is in the form of a semicircle starting from $t=2 \, s$ to $t=8 \, s$. Select the correct statement.

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The displacement of the particle varies with time according to the relation $x = \frac{k}{b}\,[1 - {e^{ - bt}}]$. Then the velocity of the particle is

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Match Column-$I$ with Column-$II$:

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The velocity of a particle moving on the $x$-axis is given by $v = x^2 + x$,where $v$ is in $m/s$ and $x$ is in $m$. Find its acceleration in $m/s^2$ when passing through the point $x = 2 \ m$.

Similar Questions

The graph shows the variation with time $t$ of velocity $v$ of an object moving along a straight line. The $a-t$ graph will be:

The speed-time graph of a particle moving along a fixed direction is shown in the figure. Obtain the distance (in $m$) traversed by the particle between $t=0\; s$ and $t=10\; s$.

The position-time graph of a particle moving along a straight line is shown,which is in the form of a semicircle starting from $t=2 \, s$ to $t=8 \, s$. Select the correct statement.

The displacement of the particle varies with time according to the relation $x = \frac{k}{b}\,[1 - {e^{ - bt}}]$. Then the velocity of the particle is

Match Column-$I$ with Column-$II$:

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