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Physics · MOTION IN A STRAIGHT LINE

हिन्दी

Consider the following statements regarding motion in a straight line: (A) The slope of the position-time graph gives velocity. (B) The area under the velocity-time graph gives displacement. (C) The slope of the velocity-time graph gives acceleration. (D) The area under the acceleration-time graph gives distance. Which of the above statements are correct?

  1. (B) and (D) only
  2. (A) and (C) only
  3. (A), (B) and (C) only
  4. All four (A), (B), (C) and (D)

Correct answer · Option 3

(A), (B) and (C) only

Explanation

Statements (A), (B), and (C) are correct definitions. Statement (D) is incorrect because area under a-t graph gives change in velocity, not distance.

Related questions

A particle moves along a straight line such that its position \( x \) at time \( t \) is given by \( x = t^3 - 6t^2 + 9t + 5 \). At what time(s) is the velocity of the particle zero?→Match List-I with List-II for motion under gravity (ball thrown vertically upward with initial speed \( v_0 \)): List-I List-II A Time taken to reach peak height I \( v_0 \) B Maximum height reached above launch point II \( \frac{2 v_0}{g} \) C Total time of flight to return to launch level III \( \frac{v_0}{g} \) D Speed upon returning to launch level IV \( \frac{v_0^2}{2g} \) Choose the correct answer from the options given below:→Match List-I with List-II regarding graph features in one-dimensional motion: List-I List-II A Position-time curve concave upwards (\( d^2x/dt^2 > 0 \)) I Net displacement over time interval B Position-time curve concave downwards (\( d^2x/dt^2 < 0 \)) II Motion with negative acceleration turning back after stopping C v-t graph with negative slope crossing time axis III Motion with positive acceleration (\( a > 0 \)) D Area under v-t graph between \( t_1 \) and \( t_2 \) IV Motion with negative acceleration (\( a < 0 \)) Choose the correct answer from the options given below:→A particle moves along a straight line with uniform acceleration \( a \). Its velocities at two points A and B are \( v_A = 10 \text{ m/s} \) and \( v_B = 30 \text{ m/s} \) respectively. Calculate the velocity of the particle as it passes through the midpoint C of the segment AB.→
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