Question

The distance x covered by a body moving in a straight line in time t is given by the relation
2x ² + 3x = t
if v is the velocity of body at a certain instant of time, its acceleration will be :
options :
(a) -v³
(b) -2v³
(c) -3v³
(d) -4v³
plss answer this question with a solution.. the best answer will be marked as THE BRAINLIEST

Answer 1

Answer:

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Answer 2

The acceleration of the body is $-4v^3$.

Explanation:

The distance x covered by a body moving in a straight line in time t is given by the relation :

2x² + 3x = t

On differentiating above equation wrt t we get :

$4x\dfrac{dx}{dt}+3\dfrac{dx}{dt}=1$

Since, $\dfrac{dx}{dt}=v$

$4xv+3v=1$

$v=\dfrac{1}{4x+3}$

Since, $\dfrac{dv}{dt}=a$ (acceleration)

So, $4vx+3v=1$

$4x=\dfrac{1}{v}-3$

Again differentiating above equation, we get :

$4v=-\dfrac{1}{v^2}\dfrac{dv}{dt}$

$\dfrac{dv}{dt}=-4v^3$

So, the acceleration of the body is $-4v^3$. Hence, this is the required solution.

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Kinematics

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