First slide

Rectilinear Motion

Question

For motion of an object along the x-axis, the velocity v depends on the displacement x as $v = 3 x^{2} - 2 x$ , then what is the acceleration at x = 2 m.

Moderate

A

48 ${ms}^{- 2}$
B

80 ${ms}^{- 2}$
C

18 ${ms}^{- 2}$
D

10 ${ms}^{- 2}$

Solution

Given $v = 3 x^{2} - 2 x$ ; differentiating v, we get
$\begin{array}{l} \frac{dv}{dt} = (6 x - 2) \frac{dx}{dt} = (6 x - 2) v \\ \Rightarrow a = (6 x - 2) (3 x^{2} - 2 x) \end{array}$
Now put x = 2 m
$\Rightarrow a = (6 \times 2 - 2) (3 (2)^{2} - 2 \times 2) = 80 {ms}^{- 2}$

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