Displacement , Velocity & Acceleration
Displacement
Definition: The change in location of an object
SI unit: Meter[m]
Formulae: Displacement[m] = Velocity[m/s] * time[s]
Graph: Displacement = area under velocity-time graph
Velocity
Definition: The speed of an object with a direction
SI unit: Meter per Second [m/s]
Formulae: Velocity[m/s] = Displacement[m] / Time[s]
Acceleration
Definition: Rate of change in velocity with time
SI unit: Meter per second ^2 [m/s^2]
Formulae: (final velocity - initial velocity)/time
Graph: Acceleration = Gradient under velocity/time graph
Graph
Velocity time graph
Gradient = Acceleration
Area under curve = Displacement
Displacement time graph
Gradient = Velocity
Velocity = differentiating displacement
Acceleration = differentiating velocity
Differentiation
Original Equation: displacement
1st differentiation on displacement = velocity
2nd differentiation on velocity = acceleration
Important formulae
velocity = initial velocity + acceleration * time
Final displacement = initial displacement + (initial velocity x time) + 1/2 (acceleration x time^2)
Velocity^2 = initial velocity^2 + 2 acceleration (final displacement - initial displacement)