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  4. A body is moving according to the equation x=a t+b t2-c t3 where x= displacement and a, b and c are constants. The acceleration of the body is

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Q. A body is moving according to the equation $x=a t+b t^{2}-c t^{3}$ where $x=$ displacement and $a, b$ and $c$ are constants. The acceleration of the body is

Motion in a Straight Line

Solution:

$x=a t+b t^{2}-c t^{3} ; v=\frac{d x}{d t}=a+2 b t-3 c t^{2}$
Acceleration $=\frac{d v}{d t}=2 b-6 c t$