(D) Given acceleration $a = \frac{dv}{dt} = 3t^2 + 2t + 2$.To find the velocity $v$,we integrate the acceleration with respect to time: $dv = (3t^2 +

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(D) Given acceleration $a = \frac{dv}{dt} = 3t^2 + 2t + 2$.To find the velocity $v$,we integrate the acceleration with respect to time: $dv = (3t^2 + 2t + 2)dt$.Integrating both sides with the given limits: $\int_{v_0}^{v} dv = \int_{0}^{t} (3t^2 + 2t + 2) dt$.Given $v_0 = 2\,m/s$ at $t = 0$,we have: $v - 2 = [t^3 + t^2 + 2t]_0^2$.Substituting the upper limit $t = 2$: $v - 2 = (2^3 + 2^2 + 2(2)) - 0$.$v - 2 = 8 + 4 + 4 = 16$.$v = 16 + 2 = 18\,m/s$.

Class 11 Physics Motion in Straight Line Uniformly Accelerated Motion

Medium

The acceleration $a$ in $m/s^2$ of a particle is given by $a = 3t^2 + 2t + 2$,where $t$ is the time in seconds. If the particle starts with an initial velocity $v = 2\,m/s$ at $t = 0$,then the velocity at the end of $t = 2\,s$ is $............m/s$.

A
$12$
B
$14$
C
$16$
D
$18$

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Class 11

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Chapter

Motion in Straight Line

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Uniformly Accelerated Motion

The stopping distance of a vehicle moving with a given acceleration is proportional to the ....... of its speed.

Easy

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If the velocity of a particle moving along the $x-$ axis is given by $v = k\sqrt{x}$,then which of the following is true? ($a$ is acceleration)

Medium

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The initial velocity of the particle is $10 \ m/s$ and its retardation is $2 \ m/s^2$. The distance moved by the particle in the $5^{th}$ second of its motion is .......... $m$.

Easy

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The velocity of a car accelerating uniformly increases from $20 \ m/s$ to $80 \ m/s$ while covering a distance of $200 \ m$. The time taken is $.... \ s$.

Easy

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$A$ body is moving with a uniform velocity of $8\,m/s$. When the body just crosses another body,the second body starts from rest and moves with a uniform acceleration of $4\,m/s^2$. The time after which the two bodies meet will be $...........\,s$.

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The acceleration $a$ in $m/s^2$ of a particle is given by $a = 3t^2 + 2t + 2$,where $t$ is the time in seconds. If the particle starts with an initial velocity $v = 2\,m/s$ at $t = 0$,then the velocity at the end of $t = 2\,s$ is $............m/s$.

Similar Questions

The stopping distance of a vehicle moving with a given acceleration is proportional to the ....... of its speed.

If the velocity of a particle moving along the $x-$ axis is given by $v = k\sqrt{x}$,then which of the following is true? ($a$ is acceleration)

The initial velocity of the particle is $10 \ m/s$ and its retardation is $2 \ m/s^2$. The distance moved by the particle in the $5^{th}$ second of its motion is .......... $m$.

The velocity of a car accelerating uniformly increases from $20 \ m/s$ to $80 \ m/s$ while covering a distance of $200 \ m$. The time taken is $.... \ s$.

$A$ body is moving with a uniform velocity of $8\,m/s$. When the body just crosses another body,the second body starts from rest and moves with a uniform acceleration of $4\,m/s^2$. The time after which the two bodies meet will be $...........\,s$.

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