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  4. If s=2t3-6t2+at+5 is the distance travelled by a particle at time t and if the velocity is - 3 when its acceleration is zero, then the value of a is

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Q. $If\,s=2t^{3}-6t^{2}+at+5$ is the distance travelled by a particle at time $t$ and if the velocity is $ - 3$ when its acceleration is zero, then the value of $a$ is

KEAMKEAM 2015Application of Derivatives

Solution:

Given, $s=2 t^{3}-6 t^{2}+a t+5$
Velocity, $V=\frac{d s}{d t}=6 t^{2}-12 t+a$
Acceleration, $A=\frac{d^{2} s}{d t^{2}}=12 t-12$
Since, $A=0$
$\Rightarrow 12 t-12=0$
$\Rightarrow t=1$
At $t=1$,
$V=6-12+a=a-6$
It is given that, at $A=0, V=-3$
$\Rightarrow a-6=-3$
$\Rightarrow a=3$