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Which of the following curves possibly represent one-dimensional motion of a particle?

Choose the correct answer from the options given below:

The displacement \( x \) versus time graph is shown below.

(A) The average velocity during \( 0 \) to \( 3 \, \text{s} \) is \( 10 \, \text{m/s} \)
(B) The average velocity during \( 3 \) to \( 5 \, \text{s} \) is \( 0 \, \text{m/s} \)
(C) The instantaneous velocity at \( t = 2 \, \text{s} \) is \( 5 \, \text{m/s} \)
(D) The average velocity during \( 5 \) to \( 7 \, \text{s} \) and instantaneous velocity at \( t = 6.5 \, \text{s} \) are equal
(E) The average velocity from \( t = 0 \) to \( t = 9 \, \text{s} \) is zero
Choose the correct answer from the options given below:

A person travelling on a straight line moves with a uniform velocity \( v_{1} \) for a distance \( x \) and with a uniform velocity \( v_{2} \) for the next \( \dfrac{3}{2} x \) distance. The average velocity in this motion is \( \dfrac{50}{7} \, \text{m / s} \). If \( v_{1} \) is \( 5 \, \text{m/ s} \) then \( v_{2} = \underline{\hspace{1cm}} \, \text{m / s} \).

The motion of an airplane is represented by velocity-time graph as shown below. The distance covered by airplane in the first \( 30.5 \) second is ______ km.

A particle moves along the \( x \)-axis and has its displacement \( x \) varying with time \( t \) according to the equation:
\( x = c_{0}\left( t^{2} - 2 \right) + c (t - 2)^{2} \)
where \( c_{0} \) and \( c \) are constants of appropriate dimensions.
Then, which of the following statements is correct?

Two cars \( P \) and \( Q \) are moving on a road in the same direction. Acceleration of car \( P \) increases linearly with time whereas car \( Q \) moves with a constant acceleration. Both cars cross each other at time \( t = 0 \), for the first time. The maximum possible number of crossing(s) (including the crossing at \( t = 0 \)) is _______.

A river is flowing from west to east direction with speed of \( 9 \, \text{km h}^{-1} \). If a boat capable of moving at a maximum speed of \( 27 \, \text{km h}^{-1} \) in still water, crosses the river in half a minute, while moving with maximum speed at an angle of \( 150^\circ \) to direction of river flow, then the width of the river is:

An object with mass \( 500 \, \text{g} \) moves along \( x \)-axis with speed \( v = 4\sqrt{x} \, \text{m}/\text{s} \). The force acting on the object is:

The velocity-time graph of an object moving along a straight line is shown in figure. What is the distance covered by the object between \( t = 0 \) to \( t = 4 \,\text{s} \)?

The position vector of a moving body at any instant of time is given as \( \vec{r} = (5 t^{2}\hat{i} - 5 t \hat{j}) \,\text{m} \). The magnitude and direction of velocity at \( t = 2 \,\text{s} \) is:

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JEE Main 2025 28th Jan Evening shift

The velocity-time graph of an object moving along a straight line is shown in figure. What is the distance covered by the object between \( t = 0 \) to \( t = 4 \,\text{s} \)?