a. Standard:
The standard equation of motion under gravity is given by
x = x0 + v0t + (1/2)gt^2 Where:
- x is the final displacement of the object at time t.
- x0 is the initial displacement of the object at time t=0.
- v0 is the initial velocity of the object at time t=0.
- g is the acceleration due to gravity (9.8 m/s^2 on the surface of the Earth).
- t is the time elapsed.
b. Freely falling:
Freely falling objects are objects that are in a state of constant acceleration due to gravity and are not subject to any other forces. The equation of motion for a freely falling object can be derived from the standard equation of motion by setting the initial velocity to zero (v0 = 0):
x = x0 + (1/2)gt^2
Where:
- x is the final displacement of the object at time t.
- x0 is the initial displacement of the object at time t=0.
- g is the acceleration due to gravity (9.8 m/s^2 on the surface of the Earth).
- t is the time elapsed.
c. Projected vertically down:
A body projected vertically downwards is an object that is being dropped from some height and is subject to only the force of gravity. The equation of motion for a body projected vertically downwards can be derived from the standard equation of motion by setting the initial velocity to zero (v0 = 0) and the initial height to the height from which the object was dropped (x0):
x = x0 + (1/2)gt^2
Where:
- x is the final displacement of the object at time t.
- x0 is the initial height from which the object was dropped.
- g is the acceleration due to gravity (9.8 m/s^2 on the surface of the Earth).
- t is the time elapsed.
d. Projected vertically up:
A body projected vertically upwards is an object that is being thrown upwards and is subject to only the force of gravity. The equation of motion for a body projected vertically upwards can be derived from the standard equation of motion by setting the initial velocity to the upward velocity with which the object was thrown (v0) and the final velocity to zero (v = 0):
x = x0 + v0t - (1/2)gt^2
Where:
- x is the final displacement of the object at time t.
- x0 is the initial displacement of the object at time t=0.
- v0 is the upward velocity with which the object was thrown.
- g is the acceleration due to gravity (9.8 m/s^2 on the surface of the Earth).
- t is the time elapsed.