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  4. The acceleration of a particle increases linearly with time t as 6 t . If the initial velocity of the particle is zero and the particle starts from the origin, then the distance travelled by the particle in time t will be

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Q. The acceleration of a particle increases linearly with time $t$ as 6 $t$ . If the initial velocity of the particle is zero and the particle starts from the origin, then the distance travelled by the particle in time $t$ will be

NTA AbhyasNTA Abhyas 2020Motion in a Straight Line

Solution:

We know that $a=\frac{d v}{d t}$
Then according to the question
$\frac{d v}{d t}=6t$ or $dv=6tdt,v=\frac{6 t^{2}}{2}=3t^{2}$ ,
$Also, dx=3t^{2}dt \, \Rightarrow \, x=3\frac{t^{3}}{3}=t^{3}$