Question

The velocity of a particle is given by the expression
v(x)= 3x2 - 4x
where, x is distance covered by the particle. The
expression for acceleration is
(a) (3x² - 4x)(6x - 4) (b) 6(3x² - 4x)
(c) (6x - 4)
(d) (3x2 - 4x)6x​

Answer 1

Given:

Velocity expression :

$v(x) = 3 {x}^{2} - 4x$

To find:

Acceleration expression ?

Calculation:

Acceleration (a) will be :

$\therefore \: a = \dfrac{dv}{dt}$

• Using Chain Rule of Differentiation:

$\implies \: a = \dfrac{dv}{dx} \times \dfrac{dx}{dt}$

$\implies \: a = v\dfrac{dv}{dx}$

$\implies \: a = (3 {x}^{2} - 4x) \dfrac{d(3 {x}^{2} - 4x) }{dx}$

$\implies \: a = (3 {x}^{2} - 4x)(6x - 4)$

So, the correct expression of acceleration is

a = (3x²-4x)(6x-4)