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Physics · MOTION IN A STRAIGHT LINE

हिन्दी

Consider the following characteristics of motion along a straight line: (A) Average velocity is the displacement divided by the total time interval. (B) Instantaneous velocity is the derivative of position with respect to time. (C) The area under the velocity-time graph represents acceleration. (D) In uniform motion, instantaneous speed equals average speed. Which of the above statements are correct?

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

Correct answer · Option 4

(A), (B) and (D) only

Explanation

Statements (A), (B), and (D) are correct definitions and properties. Statement (C) is false because the area under v-t graph represents displacement, not acceleration.

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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