Question

If the velocity-time graph has the shape AMB, what would be the shape of the corresponding acceleration-time graph ?

• A.

  

• B.

  

• C.

  

• D.

  

Answer 1

The Correct Option is B

To solve this question, we need to analyze the relationship between the velocity-time (v-t) graph and the acceleration-time (a-t) graph.

1. Understanding Basic Concepts:

   • The slope of a velocity-time graph represents acceleration. Therefore, at any point on the v-t graph, the acceleration can be found by calculating the slope of the tangent to the curve at that point.
   • If the slope is constant, acceleration is constant; if the slope is changing, the acceleration is changing as well.

2. Analyze the Given Graph:

   • The velocity-time graph mentioned here is represented by three segments: AMB.
   • Segment AM: This part of the curve is inclined. A straight-line segment with a positive slope indicates constant acceleration.
   • Segment MB: This is flat (horizontal). A horizontal line indicates zero acceleration as the velocity remains constant.

3. Derive the Shape of the Acceleration-Time Graph:

   • For segment AM (increasing v-t line), the a-t graph will show a positive constant value, indicating that the object is accelerating at a constant rate.
   • For segment MB (horizontal line), the a-t graph will show zero acceleration because the velocity is constant.

As per the above analysis, the correct acceleration-time graph corresponds to the image provided above, which shows a constant positive acceleration followed by zero acceleration.