When a body changes its position, we say that the body has moved. There are different types of movement.
There is circular movement - linear movement - and oscillatory movement.
What concerns us now is movement in a straight line. The body may move forward and backward or up and down.
We say about this movement movement in a straight line or movement in one dimension.
Motion chart
The motion of an object can be described by successive images taken of the object at equal intervals of time.
he runner is moving in a straight line and the speed is constant because he covers equal distances in equal times.
The ball follows a Parabolic cut path and the motion is in two dimensions.
The motion of a body can be described by considering the body as a point taken from the middle of the body and through the particle model we determine the motion of the body.
The particle model indicates that the speed is constant because it covers equal distances in equal times and the motion is in a straight line.
The particle model indicates that the speed is increasing because it covers increasing distances in equal times and the motion is in a straight line.
The particle model indicates that the speed is decreasing because it covers decreasing distances in equal times and the motion is in a straight line.
Body location
When we describe the motion of an object, we define it relative to a point that is considered fixed, and the location is defined relative to a reference point or an agreed-upon reference location within a frame of reference called (the origin point). The distance of the object from this point is called the location. The location of the particle is determined only by choosing a reference point that we consider the origin point of reference.
Location: a vector quantity that may be positive or negative.
The location is to the right of the reference point, so the location is positive.
The location is to the left of the reference point, so the location is negative.
Physical quantities are divided into two types
vector quantities
Standard quantities
It has a magnitude and a direction.
has a magnitude but do not have direction.
like
velocity
Displacement
Accelerationع
like
Time
Temperature
Distance
The concept of displacement and distance
distance :It is a positive numerical quantity and expresses "the distance traveled by the body during its movement." In the case of movement in a straight line, the distance is the distance that the body has traveled numerically.
Example: Ahmed moved from location 2- to location 6+, then changed his direction and moved to location 3+. The distance traveled is equal to
\[s=8+3=11 m\]
displacement
: It is a vector quantity and is the difference between the point where the body is located at the end of its movement and the point where it started
In other words, displacement is the change in the position of an object during its movement.
When a body moves from its initial position
\[X_i\]
to its final position
\[X_f\]
The displacement is given by the following relation:
\[\Delta {\mathbf{X} }= X_f – X_i \]
Example: Ahmed moved from position 2- to position 6+, then changed his direction and moved to position 3+. The displacement that Ahmed moved is equal to
\[\Delta X = X_f – X_i=+3 - (- 2)=+5\]The positive sign indicates that the displacement is in the positive direction.
In this simulation we will learn about distance and displacement in one dimension.
Solved example A car moved from location
[150\;m\] to location
[60\;m\], then the displacement covered is equal to
الحل \[\Delta X = X_f – X_i=60 - (150)=- 90 m \]
Solved example
Calculate the displacement and distance if Ahmed moved according to the following diagram.ي
\[A\Rightarrow D\Rightarrow B \Rightarrow C \]
the solution We define the origin point of the movement wherever you want.
and let it be at the position\[B\]
the solution We define the origin point of the movement wherever you want.
And let it be at the place \[B\]
\[S=140+40 +140 =320 m \]
\[X_i=-180 m , X_f=-140 m \]
\[\Delta X = X_f – X_i=(-140 )- (-180)=+40 m \]
1
Majid moved from Ajman to Umm Al-Quwain and then changed his direction towards Sharjah, passing through the city of Ajman. Using the following diagram, Calculate the distance and displacement covered...
Constant velocity motion experiment and plotting the( position-time) graph In this simulation, move the velocity indicator to an appropriate value.
Solved example
In a running race, successive photos of a runner were taken every two seconds, as shown in the figure below. The following photos were produced, and the relationship between location and time was drawn. The following graph was produced:
From which position did the runner's movement study begin, and at which position did the study end? \[x_i= 4 m, x_f= 26 m\]
What is the distance covered by the runner? \[s=6+10=16 m\]
What is the displacement? \[\Delta x= x_f−x_i=26-4=22 m\]
Note that the distance and displacement have the same value because the runner did not change direction. What is the reason for the change in the slope of the graph? The reason is due to the change in the runner's speed; in the sixth second, the runner changed speed, but it remained constant.
Play and learn
2
The following graph shows the relationship between position and time. For the motion of a bicycle, the distance and displacement covered are
A vector quantity whose direction is always the direction of displacement.
Unit of measure \[\frac{m}{s}\]
Unit of measure\[\frac{m}{s}\]
Solved example The position-time relationship for a bicycle is plotted as in the figure below. The distance covered during the entire period is equal to The bicycle moved from position 4 to position 12 and covered a distance of \[8\;m\] then changed direction and moved from position 12 to position 0, thus covering a distance of \[12\;m\] then continued moving in the negative direction and moved to position -8, thus covering \[8\;m\] L=8+12+8=28 m The displacement covered during the entire period The initial position of the motion (xi= 4 m) The final position of the motion (xf= -8 m) \[\Delta 𝑥= 𝑥_𝑓−𝑥_𝑖=-8-4=-12 m\] Calculating the average velocity \[\vec v =\frac{\vec X_f-\vec X_i}{t_f-t_i}= \frac{-12}{16-0}=-0.75 \frac{m}{S}\] Calculating the speed \[ v =\frac{L}{t_f-t_i}=\frac{28}{16-0}=1.75\frac{m}{S}\]
Experiment of motion at constant speed and drawing the graph (Position - Time) (Velocity - Time)(Acceleration - Time)
The relationship between average speed and slope of the graph (position - time)
The graph below shows the position-time relationship for a bicycle moving at a constant speed.
\[ X_i= 0.0 , X_f = 24 \]\[\Delta 𝑥= X_𝑓−X_𝑖=24-0=24 m\] \[\vec v =\frac{\vec X_f-\vec X_i}{t_f-t_i}= \frac{24}{12-0}=2 \frac{m}{S}\]
Calculate the slope of the graph and write the equation of motion from the graph.
Click here to view the learning outcomes
Click here to show the solution method
Click here to show the solution method
Click here to show the solution method
Click here to show the solution method
Click here to show the solution method
Click here to show the solution method
Click here to show the solution method
){kind=link}
0 Comments