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

Question

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 (A) a+2 b t (B) 2 b+6 c t (C) 2 b-6 c t (D) 3 b-6 c t2

Tardigrade Admin · Accepted Answer

x=a t+b t2-c t3 ; v=(d x/d t)=a+2 b t-3 c t2 Acceleration =(d v/d t)=2 b-6 c t

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

$a + 2 b t$

$2 b + 6 c t$

$2 b - 6 c t$

$3 b - 6 c t^{2}$

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

Q. A body is moving according to the equation x=at+bt2−ct3 where x= displacement and a,b and c are constants. The acceleration of the body is

a+2bt

2b+6ct

2b−6ct

3b−6ct2