List of top Physics Questions on Particle Motion

A rod has length \( L \). The linear mass density is \( 2x \, \text{kg/m} \), where \( x \) is the distance from the left end. The center of mass of the rod from the left end lies at a distance of
A graph shows the velocity of an object as a function of time. Describe the motion of the object in detail, including its acceleration and displacement, at different points in time. What does the area under the curve represent?
A ball is released from the top of a tower of height \( h \) meters. It takes \( T \) seconds to reach the ground. What is the position of the ball above the ground in \( T/5 \) seconds?
The velocity of a particle is given by the equation \( v(x) = 3x^2 - 4x \), where \( x \) is the distance covered by the particle. The expression for its acceleration is:

A ball of mass m is falling freely under gravity through a viscous medium in which the drag force is proportional to the instantaneous velocity \(v\) of the ball. Neglecting the buoyancy force of the medium, which one of the following figures best describes the variation of \(v\) as a function of time \(t\)? 

If the motion of a particle is described by \( x = 5 \cos(8\pi t), y = 5 \sin(8\pi t) \) and \( z = 5t \), then the trajectory of the particle is
A graph shows the velocity of an object as a function of time. Describe the motion of the object in detail, including its acceleration and displacement, at different points in time. What does the area under the curve represent?