The figure shown above gives the time (t) versus position (x) graphs o

The figure shown above gives the time (t) versus position (x) graphs of three objects A, B and C. Which one of the following is the correct relation between their speeds $V_A$, $V_B$ and $V_C$, respectively at any instant (t > 0)?

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This question was previously asked in

UPSC NDA-1 – 2019

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The speeds of the three objects are represented by the slope of their position-time graphs. The correct relation between their speeds is $V_A > V_B > V_C$.

– In a position-time (x-t) graph, the velocity (speed if motion is in one direction without change in direction) is given by the slope of the graph ($\Delta x / \Delta t$).
– A steeper slope indicates a higher speed, and a less steep slope indicates a lower speed.
– Examining the graph, the line for object A has the steepest slope.
– The line for object B has a slope less steep than A but steeper than C.
– The line for object C has the least steep slope.
– Since all slopes are positive, the objects are moving in the positive direction. The magnitude of the slope represents the speed.

All three graphs are straight lines, indicating that the objects are moving with constant velocities (uniform motion). If the lines were curved, the slope would change over time, indicating changing velocity (acceleration).

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