Answer:
Certainly! Let's break down parts E, F, and G based on the information typically covered in a physics problem involving motion in three dimensions.
Part E: Sketching Graphs
v
x
vs.
t: This graph represents the velocity of the object in the x-direction over time.
If the object has constant velocity
=
0
v
x
=v
x0
, the graph would be a horizontal line at
0
v
x0
.
If
v
x
changes with time, the graph would show how
v
x
varies over the given time interval.
v
y
vs.
t: This graph represents the velocity of the object in the y-direction over time.
Similar to
v
x
, if
v
y
is constant, the graph would be a horizontal line.
If
v
y
changes, the graph would show that variation.
v
z
vs.
t: This graph represents the velocity of the object in the z-direction over time.
Again, if
v
z
is constant, the graph would be a horizontal line.
If
v
z
varies, the graph would indicate how it changes over time.
Typically, these graphs could include different scenarios such as constant velocity, acceleration, or even deceleration, depending on the specific motion described in the problem.
Part F: Acceleration
⃗
a
as a Function of Time
t
The acceleration
⃗
a
of the object as a function of time
t can be described in vector form
⃗
=
(
,
,
)
a
=(a
x
,a
y
,a
z
), where:
a
x
is the acceleration in the x-direction,
a
y
is the acceleration in the y-direction,
a
z
is the acceleration in the z-direction.
Each component
a
x
,
a
y
, and
a
z
can vary depending on external forces acting on the object. For example:
If the object is in free fall near the Earth's surface,
a
y
could be approximately
−
9.8
−9.8 m/s² (acceleration due to gravity in the negative y-direction),
a
x
and
a
z
could be zero if there are no forces acting in those directions.
Part G: Description of Motion in x, y, and z Directions
To describe the motion accurately in each direction:
In the x-direction: Analyze how
v
x
changes over time. If
v
x
is constant, the object moves at a steady speed in the x-direction. If
v
x
changes, note whether it accelerates or decelerates.
In the y-direction: Consider how
v
y
changes over time. If
v
y
is constant, the object moves at a steady speed vertically. If
v
y
changes, describe if it's accelerating upwards (positive
a
y
) or downwards (negative
a
y
).
In the z-direction: Examine how
v
z
changes over time. If
v
z
is constant, the object moves at a steady speed in the z-direction. If
v
z
changes, describe if it's accelerating upwards (positive
a
z
) or downwards (negative
a
z
).
Combine these descriptions to give a comprehensive understanding of how the object moves through space in all three dimensions.
By following these steps, you should be able to complete parts E, F, and G of your homework involving motion in three dimensions. If you have specific numerical data or equations given in the problem, those would be used to plot the graphs and derive the acceleration and motion descriptions more precisely.