Solved: PHYSICS Question for NEET

NEET PHYSICSEasy

The velocity ( $v$ )-time ( $t$ ) plot of the motion of a body is shown below: The acceleration ( $a$ )-time ( $t$ ) graph that best suits this motion is:

Option 1

Option 2

Option 3

Option 4

Step-by-Step Solution

Principle: The acceleration of a particle is defined as the rate of change of velocity with respect to time ( $a = \frac{dv}{dt}$ ). Geometrically, this corresponds to the slope of the velocity-time ( $v-t$ ) graph .
Analysis: To determine the correct acceleration-time ( $a-t$ ) graph from a given $v-t$ graph, one must analyze the slope of the $v-t$ curve at various intervals:

Positive Slope: If the $v-t$ line goes upwards (velocity increases), the acceleration is positive.
Negative Slope: If the $v-t$ line goes downwards (velocity decreases), the acceleration is negative.
Zero Slope: If the $v-t$ line is horizontal (constant velocity), the acceleration is zero.
Constant Slope: If the $v-t$ graph consists of straight lines, the acceleration is constant during those intervals (represented by horizontal lines on the $a-t$ graph).

Conclusion: The correct $a-t$ graph will depict the values of these slopes corresponding to the time intervals in the $v-t$ plot.

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