derive the expression for a time of a flight of a particle
If you are asking regarding Time of Flight for a Projectile , then here is how you can derive it's equation.
Let the velocity with which the projectile was fired = V
Let the angle which the projectile makes with Horizontal = θ (theta)
So velocity of particle in Y axis = V sin θ
Formula for the Height (Displacement) achieved by an object when thrown upwards is: S = ut + (1/2) at^2
From the above formula, displacement (S) for a projectile in Y-axis = 0 (since it goes up and then again falls back to ground).
So, 0 = ut + (1/2) at^2
⇒ 0 = V sinθt + (1/2) at^2
⇒ t = (2V sin θ)/g
So time of flight for a projectile is: T = (2V sin θ)/g
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