(C) Given acceleration $a = \frac{dv}{dt} = bt$.Integrating with respect to time to find velocity $v$:$\int_{v_0}^{v} dv = \int_{0}^{t} bt \, dt$$v -

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(C) Given acceleration $a = \frac{dv}{dt} = bt$.Integrating with respect to time to find velocity $v$:$\int_{v_0}^{v} dv = \int_{0}^{t} bt \, dt$$v - v_0 = \frac{1}{2}bt^2$$v = v_0 + \frac{1}{2}bt^2$Now,since $v = \frac{ds}{dt}$,we integrate to find displacement $s$:$\int_{0}^{s} ds = \int_{0}^{t} (v_0 + \frac{1}{2}bt^2) dt$$s = [v_0t + \frac{1}{2}b \cdot \frac{t^3}{3}]_0^t$$s = v_0t + \frac{1}{6}bt^3$.

Class 11 Physics Motion in Straight Line Uniformly Accelerated Motion

Difficult

The acceleration of an object increases with time as $a = bt$. The object starts from the origin with an initial velocity $v_0$. Find the distance traveled by the object in time $t$.

A
$v_0t + \frac{1}{3}bt^2$
B
$v_0t + \frac{1}{3}bt^3$
C
$v_0t + \frac{1}{6}bt^3$
D
$v_0t + \frac{1}{2}bt^2$

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Class 11 Questions

Class 11

Physics Questions

Chapter

Motion in Straight Line

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Uniformly Accelerated Motion

$A$ particle moving with a uniform acceleration travels $24 \ m$ and $64 \ m$ in the first two consecutive intervals of $4 \ sec$ each. Its initial velocity is......$m/sec$.

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$A$ body starts from rest with uniform acceleration and its velocity at a time of $n$ seconds is $v$. The total displacement of the body in the $n^{\text{th}}$ and $(n-1)^{\text{th}}$ seconds of its motion is:

MediumAP EAMCET 2025

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For a body moving with uniform acceleration along a straight line, the variation of its velocity $(v)$ with position $(x)$ is best represented by:

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$A$ particle is moving along a straight line with constant acceleration. At the end of the $10^{th}$ second,its velocity becomes $20 \, m/s$,and in the $10^{th}$ second,it travels a distance of $10 \, m$. Then the acceleration of the particle will be ........ $m/s^2$.

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$A$ car accelerates from rest at a constant rate of $2 \ m/s^2$ for some time. Then it retards at a constant rate of $4 \ m/s^2$ and comes to rest. If it remains in motion for $3 \ s$,then the total displacement covered by it is $.... \ m$.

Medium

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The acceleration of an object increases with time as $a = bt$. The object starts from the origin with an initial velocity $v_0$. Find the distance traveled by the object in time $t$.

Similar Questions

$A$ particle moving with a uniform acceleration travels $24 \ m$ and $64 \ m$ in the first two consecutive intervals of $4 \ sec$ each. Its initial velocity is......$m/sec$.

$A$ body starts from rest with uniform acceleration and its velocity at a time of $n$ seconds is $v$. The total displacement of the body in the $n^{\text{th}}$ and $(n-1)^{\text{th}}$ seconds of its motion is:

For a body moving with uniform acceleration along a straight line, the variation of its velocity $(v)$ with position $(x)$ is best represented by:

$A$ particle is moving along a straight line with constant acceleration. At the end of the $10^{th}$ second,its velocity becomes $20 \, m/s$,and in the $10^{th}$ second,it travels a distance of $10 \, m$. Then the acceleration of the particle will be ........ $m/s^2$.

$A$ car accelerates from rest at a constant rate of $2 \ m/s^2$ for some time. Then it retards at a constant rate of $4 \ m/s^2$ and comes to rest. If it remains in motion for $3 \ s$,then the total displacement covered by it is $.... \ m$.

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