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Physics · MOTION IN A STRAIGHT LINE

हिन्दी

What does the area under a velocity-time (\( v-t \)) graph for any moving object represent?

  1. Acceleration

  2. Instantaneous speed

  3. Position

  4. Displacement

Correct answer · Option 4

Displacement

Explanation

The area under the \( v-t \) curve represents the integral of velocity with respect to time, which gives the displacement over a given time interval.

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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