Particle Motion Under Gravity
Example 5.3: Particle Motion with Constant Acceleration
This simulation demonstrates the motion of a particle under constant gravitational force.
Example
Question:
The motion of a particle of mass \(m\) is described by \(y = ut + \frac{1}{2}gt^2\).
Find the force acting on the particle.
Solution:
We know: \[ y = ut + \frac{1}{2}gt^2 \] Now, \[ v = \frac{dy}{dt} = u + gt \] Acceleration: \[ a = \frac{dv}{dt} = g \] Then the force acting on the particle is given by: \[ F = ma = mg \] Thus, the given equation describes the motion of a particle under acceleration due to gravity, and \(y\) is the position coordinate in the direction of \(g\).



