If a particle moving in a straight line, the following graph shows

F1 Jayesh 8.5.20 Pallavi D2

  1. Acceleration of particle is non uniform
  2. Acceleration is constant
  3. Particle is decelerating uniformly
  4. The data from graph is insufficient

Answer (Detailed Solution Below)

Option 2 : Acceleration is constant
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Detailed Solution

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The correct answer is Acceleration is constant.

Concept:

  •  The rate of change of velocity of a body is called the acceleration of that body.
  • It is a vector quantity that has both magnitudes as well as direction. 

\(acceleration\left( a \right) = \frac{{Change\;in\;velocity}}{{time\;taken}} = \frac{{{v_2} - {v_1}}}{{{t_2} - {t_1}}}or\frac{{dv}}{{dt}}\)

  • The slope (m) of the displacement-time graph at any point will give the instantaneous velocity at that point.
  • The slope of any graph at a point is given by: Slope (m) = tanθ
  • Where θ is the angle made by the point with the x-axis.


Explanation:

  • The given graph shows acceleration vs time graph
  • In our case, the slope of the given graph is zero since the angle (θ) in our case is zero
  • i.e., \(\tan \theta = \frac{{da}}{{dt}} \Rightarrow \frac{{da}}{{dt}} = 0\)
  • From this we can see that rate of change of acceleration is zero hence the acceleration throughout the motion must remain constant.
  • Hence option 2 is correct
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