Question

Which graph shows the correct \( v \)–\( x \) graph of a freely falling body?

• A.

  

• B.

  

• C.

  

• D.

  

Hint:

Use the kinematic equation \( v^2 = u^2 + 2a x \) to relate velocity with displacement when acceleration is uniform.

Answer 1

The Correct Option is A

For a freely falling body under gravity: \[ v^2 = u^2 + 2a x \quad \text{(when acceleration is constant)} \] If the body starts from rest (\( u = 0 \)), then: \[ v^2 = 2a x \Rightarrow v = \sqrt{2a x} \] So the \( v \)–\( x \) relationship is a square root function, producing a curve that increases with \( x \) but flattens out—matching graph (a).