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Measuring the Rate of Change of Motion

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Last updated date: 21st Jul 2024
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How do we measure the Rate of Motion?

Here we are going to learn in detail about motion. To learn about the motion and rest we have to be aware about the reference point or stationary object. To mention the condition of any object we have to first recognise its reference point and stationary object. On the reference point, the stationary object does not change position.


For example, we can consider a building and a car, then a building will always be stationary because it will not change its position. Although cars can change. So, we can say that a car is in motion. we have to consider a stationary object with respect to it.  This stationary object is generally called a reference point.


Rest and Motion

Now assume a car standing in front of the building at any location A. Let’s say that  after some time it will be at location B. It means that it has changed its position concerning the stationary object that is the house and if that car keeps on standing in position that means it has not changed its position with respect to it. Here the building is at rest so with their help we can learn about what is clearly rest and Motion.


Rest: Rest is the process when a body does not change its position in a specific interval of time with respect to the surrounding or the considered reference point, then it is called in the position of the rest.


Motion: When a body changes its position in a specific interval of time with respect to the surrounding or the considered reference point, then it is called in the position of the motion.


So from here we can say that an object which is in motion or in rest has the following characteristics.


Characteristics of a moving object

The moving object is that, which changes its position with time. As we have seen, the movement of the car can be easily seen, that is, we don't have to concentrate much. Because it covers a significant distance in a given period of time. However to know the movement of a needle of the clock hour hand we need to ensure it. This is because  motion of some of the objects is faster in comparison to others. So that we can see it happening.On the other hand,  motion of some of the objects is so slow that it can’t be seen undoubtedly.


In conclusion we can say that a wrist watch has three hands: minute, seconds and hour hand. Out of them, second-hand moves faster than others. So it is significant to observe. But to observe the motion in hour hand and minute hand we have to keep track because of moderately slow motion.


According to Newton’s first law of motion: A body tends to remain at rest or in motion until or unless an external force is applied to it. Therefore, on giving a push to a body, the body changes its position. So, the change in position of a body over time is called the motion. There are various units to measure the rate of change of motion of a body namely: Speed, average speed, velocity, average velocity, instantaneous velocity, etc. Here, the basic consideration for the measurement of rate of change of motion is time. Let’s discuss these units in detail.


Speed What do you Understand by the Term, ‘Speed’?

Speed of any body is defined as the rate of change of position of that body in any direction.

It is also defined as the distance covered by the body in a unit time in any direction. 

The formula for the same is given by:

Speed = Distance Covered / time taken  = D/T

Its unit is m/s in the mks system or SI and cm/s in the cgs system.


Types of Speed:

  1. Uniform speed: An object that covers equal distances in equal intervals of time.

  2. Variable speed:  An object that covers unequal distances in unequal intervals of time. It has a magnitude because the direction of the body is unknown. Therefore, speed is a scalar quantity.


Average Speed

When an object is moving with a variable speed, then the average speed of that object is that constant speed with which the object covers the same distance in a given time, as it does while moving with variable speed in a given time.


Average Speed Formula Physics

Average speed formula in physics is given by:               

Total distance covered/total time taken = 2 v1v2/(v1+v2)


Its unit is also m/s in the mks unit and cm/s in the cgs system.


Define Average Velocity

  • Velocity of an object is equivalent to the rate of change of displacement.

  • Where displacement is a vector quantity and is defined as the distance between the two positions of the object in a particular direction during a given time.

  • Velocity is a vector quantity as it has both magnitude (speed) and direction.

  • The value of velocity and displacement can be expressed as zero, negative or positive.

  • The average velocity is defined as the total displacement of the body divided by the total time taken.


Average Velocity  (Physics)


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If you look at the above graph, there are two points A and B.

Here, the point A corresponds to time t1 and displacement x1 while point B to time t2 and displacement x2.

Displacement of an object at time interval (tᵣ - tᵢ) =  xᵣ - xᵢ.

The formula for the average velocity is given by:           

Vav = Total displacement /Total time = Δx /Δt = xᵣ - xᵢ/ tᵣ - tᵢ..(1)


Where, 

              xᵢ = initial distance

              xᵣ =final distance

               tᵢ  = initial time

               tᵣ =  final time

If there are diverse distances let’s say d1, d2, d3….dn in different time intervals t1, t2, t3,…..tn     

Then, formula is given by,

Vav = (d1+d2+d3+....+dn)/(t1+t2+t3+....+tn)


The slope of a straight line AB is given by:                  

Vav = xᵣ - xᵢ/ tᵣ - tᵢ = tanΘ…(2)


The eq(2) states that the magnitude of average velocity of the object between two points is equal to the slope of the straight line AB joining these two points on the graph.

Average velocity formula physics

  If   u = initial velocity

        v = final velocity

Then the formula for the mean velocity is given by, 

Vmean = (u+v)/2


The average velocity equals the sum of the initial velocity and the final velocity divided by 2.


Instantaneous Velocity (Physics)

The word instant means at that very moment. 

So the instant velocity of an object in motion is calculated at a specific point(x,t).

This velocity is the limit of average velocity as the elapsed time approaches zero.

Since average velocity between two points A and B is

                                  Vav= xᵣ - xᵢ/ tᵣ - tᵢ

If time interval is small i.e., t2 -t1 = Δt and x2 - x1 =  Δx

 If Δt -> 0, the average velocity becomes instantaneous velocity.

Then,                       

Vins = lim Δx/Δt = dx/dt Δt-> 0


Hence, instantaneous velocity of the object is the first derivative of displacement with respect to time. 


Do you know?

When a body is traveling through a uniform motion along a linear path in a given direction, the magnitude of the displacement is equivalent to the actual distance traveled by the body in a given time.


Types of Motion with Explanation

On the basis of nature of movement Motion can be classified into the following categories:


Linear Motion

Linear motion is the kind of motion where we move in a straight line is called linear motion. For example, driving on straight roads is an example of linear motion.


Rotational Motion

The rotation of earth can be an example of rotational motion. We know that earth rotates on its axis which causes day and night. Its progress is an example of rotational motion because it is rotating on its axis. Hence, we can define it as the rotational motion when the body rotates about a fixed axis.


Circular motion

The motion in a circular path is called the circular motion. All of us observe roundabouts on-road everyday. Also when we go through any road, we can't go straight through it. We also take some curved roads and will also go through circular motion.


The movement of the body in a curved path is called the circular motion. one more example could be satellites orbiting around the planet.


Vibratory Motion 

Everyone must have seen someone playing the instrument guitar. So generally what happens when you hit it with your finger.The strings of the guitar vibrates and produces the sound. This motion is called vibratory motion. This motion happens due to the vibratory motion of particles. Hence,  motion is produced when the body shows to and fro movements.


Scalar and Vector Physical Quantities

We have learnt many of the physical quantities like velocity, speed, displacement etc. All these quantities can be classified under two categories. These categories are scalar and vector. It depends upon whether they provide the complete information about the magnitude  and directions or give the unfinished information like only direction.


Conclusion:

Everything and everyone around us are in motion most of the time. To understand the different types of motion is a hefty thing to do. This article explains motion, its characteristics, and types. You can peruse through this for a better understanding.

FAQs on Measuring the Rate of Change of Motion

1. How do you Find Average Speed?

Let’s take an example:

Suppose a truck travels a distance from A to B at a speed of 60 kmph and returns to A at a speed of 120 kmph. Average speed of the whole journey is:


Let AB = s,  time taken from A to B = t1 = s/60


Then, BA = s  and t2 = s/120


Total time taken = t1+ t2 = s(1/60 + 1/120) = s/40 h


Total distance = s + s =2s


So,  average speed will be:


Vav = Total distance traveled/ total time taken = 2s/ s/40 = 80 kmph.

2. What is an Example of Average Velocity?

A woman takes 60 minutes to drive 30 miles east and then 30 miles west to end up at the same place. She walks with an average speed of 60 miles divided by 60 minutes equal to 1 mile per minute or 60 mph.

3. Derive the Average Velocity Formula.

Let’s consider the equation of 2nd law of motion : 

s = ut + ½ at²


Since v = s/t 


v = (ut + ½ at²)/t


= u + at/2


= (2u + at)/2


= ((u + (u + at)/2 …..(1)


From first law of equation of motion: v = u + at putting in eq (1)


Average velocity = u + v/ 2 = (vᵣ + vᵢ)/2

4. Define scalar and vector quantities?

The quantities which depend upon the magnitude and not the direction are called scalar quantities. They are represented as their symbols. The examples of scalars are speed, distance etc. The physical quantities which generally depend upon the magnitude and also have a specific direction. They are represented by making bold to their symbols or putting an arrow on their respective symbols.

5. What is the reference point and reference frame ? What is the magnitude?

A reference point or origin is the point with which we define the position of any of the objects. An object may appear in motion  to one observer and stationary to another. A common reference frame is to make our observations easy. All substances must be in the same reference frame. The magnitude is the extent of physical quantity. In physics, we divide physical quantities in the categories of scalers and vectors. Scalars quantity has only magnitude while vectors have also direction with magnitude.