Question

The acceleration-time graph of a body is shown below. The most probable velocity-time graph of the body is

• A.

  

• B.

  

• C.

  

• D.

  

Hint:

Acceleration = slope of velocity graph. Increasing \(a\) $\Rightarrow$ curve; zero \(a\) $\Rightarrow$ straight horizontal line.

Answer 1

The Correct Option is C

Concept: \[ a = \frac{dv}{dt} \Rightarrow v = \int a \, dt \]

Step 1: Analyze acceleration graph.
Acceleration increases linearly with time, then becomes zero.

Step 2: Effect on velocity.

• Increasing acceleration $\Rightarrow$ velocity curve is concave upward (curved increase)
• Constant zero acceleration $\Rightarrow$ velocity becomes constant (horizontal line)

Step 3: Match with options.
Only option (C) shows:
• Initially curved increase
• Then constant velocity Conclusion: \[ {(C)} \]