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If the slope of velocity-time graph represents a quantity \(\beta\), then the value of \(\beta\) is 

If the slope of velocity-time graph represents a quantity \(\beta\), then the value of \(\beta\) is  Correct Answer Instantaneous acceleration

Correct option-3

Concept:-

  • Velocity of a moving object indicates how fast the position of that particle is changing with time.
  • The slope of the tangent in a graph plotted between two physical quantities is the rate of change of that quantity represented by Y-axis with respect to the change in the quantity represented by x-axis.
  • The graph between velocity and time (v-t) is very useful in the numerical analysis.
  • The v-t graph gives us the idea of displacement and acceleration.
  • By the slope of v-t graph, we can find the acceleration and 
  • By the area under v-t graph we can find displacement.

 

Explanation:-

  • The slope of velocity-time graph determines the instantaneous acceleration and its unit is m/s2.

[ alt="Instantaneous speed" src="//storage.googleapis.com/tb-img/production/21/04/Instantaneous%20speed.png" style="width: 312px; height: 282px;">

 

  • In the above figure the slope of the tangent at t = t0 represents instantaneous acceleration of the particle at that instant.

Hence, option-3 is the correct answer.

  • We can understand that v-t graph of a particle will be straight line when it is moving with a constant acceleration.

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