Question

The velocity of a particle is given by the equation $v(x) = 3x^2 - 4x$, where $x$ is the distance covered by the particle. The expression for its acceleration is:

• A. $(6x - 4)$
• B. $6(3x^2 - 4x)$
• C. $(3x^2 - 4x) (6x - 4)$
• D. $(6x - 4)^2$

Hint:

When given the velocity function, differentiate it with respect to $x$ to find the acceleration.

Answer 1

The Correct Option is C

The acceleration $a(x)$ is the rate of change of velocity with respect to time, given by the formula: $$a(x) = \frac{dv}{dt}.$$ Using the chain rule, we express this as: $$a(x) = v'(x) \cdot v(x),$$ where $v(x) = 3x^2 - 4x$. First, we differentiate $v(x)$: $$v'(x) = \frac{d}{dx}(3x^2 - 4x) = 6x - 4.$$ Now, the acceleration is: $$a(x) = (6x - 4) \cdot (3x^2 - 4x).$$