Solved: PHYSICS Question for NEET

NEET PHYSICSMedium

Acceleration-time graph of a body is shown. The corresponding velocity-time graph of the same body is:

Option 1

Option 2

Option 4

Fundamental Relation: Instantaneous acceleration ( $a$ ) is defined as the rate of change of velocity ( $v$ ) with respect to time ( $t$ ), given by the derivative $a = \frac{dv}{dt}$ .
Integral Relationship: The change in velocity is the integral of acceleration with respect to time: $v - v_0 = \int_{0}^{t} a dt$ . This means the area under the acceleration-time ( $a-t$ ) graph for a given time interval represents the change in velocity during that interval .
Graphical Interpretation:

The slope of the velocity-time ( $v-t$ ) graph at any instant represents the acceleration at that instant.
If the $a-t$ graph shows constant positive acceleration, the $v-t$ graph is a straight line with a positive slope.
If acceleration drops to zero, the $v-t$ graph becomes a horizontal line (constant velocity).

Conclusion: To identify the correct $v-t$ graph (Option 4), one must check that the slope of the velocity curve at every point corresponds to the value of the acceleration graph at that same time.

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