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The displacement-time graph of a moving particle is shown below. The instantaneous velocity of the particle is negative at the point

A

D

B

F

C

C

D

E

Step-by-Step Solution

  1. Definition of Instantaneous Velocity: The instantaneous velocity (vv) of a particle is defined as the rate of change of position with respect to time, given by the derivative v=dxdtv = \frac{dx}{dt} .
  2. Graphical Interpretation: On a displacement-time (x−tx-t) graph, the value of dxdt\frac{dx}{dt} at any specific instant corresponds to the slope of the tangent to the curve at that point .
  3. Analyzing Slope Signs:
  • A positive slope (tangent pointing up) indicates positive velocity.
  • A zero slope (horizontal tangent) indicates zero velocity.
  • A negative slope (tangent pointing down) indicates negative velocity.
  1. Conclusion: To find the point where velocity is negative, one must identify the point on the graph where the tangent has a negative slope (i.e., the curve is going downwards). Point E corresponds to a region where the displacement is decreasing with time, meaning the slope is negative.
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