Question

An object moving along x-axis with a uniform acceleration has velocity \( \vec{V} = (12\ \text{cm/s})\hat{i} \) at \( x = 3\ \text{cm} \). After 2 s, if it is at \( x = -5\ \text{cm} \), then its acceleration is:

• A. \( \vec{a} = (-16\ \text{cm/s}^2)\hat{i} \)
• B. \( \vec{a} = (11\ \text{cm/s}^2)\hat{i} \)
• C. \( \vec{a} = (-11\ \text{cm/s}^2)\hat{i} \)
• D. \( \vec{a} = (8\ \text{cm/s}^2)\hat{i} \)

Hint:

Apply the equation \( x = ut + \frac{1}{2}at^2 \) carefully, watch for sign conventions.

Answer 1

The Correct Option is A

Use kinematic equation: \[ x = ut + \frac{1}{2} a t^2 \] Given: \( x = -5 - 3 = -8\ \text{cm},\ u = 12\ \text{cm/s},\ t = 2\ \text{s} \) \[ -8 = 12 \cdot 2 + \frac{1}{2} a \cdot 4 \Rightarrow -8 = 24 + 2a \Rightarrow a = \frac{-32}{2} = -16\ \text{cm/s}^2 \]