Measuring Rate of Change Motion

Introduction

When we are moving from one position to another position, then we are said to be in motion. Motion is nothing but just a movement. Every moving object's changes their position with time. Now, it is also well known that motion is of two types, Uniform and Non-uniform. Uniform motion is constant and there is no change. However, Non- uniform motion is an example of changes in motion.

Now, we will learn how an object changes their position with time.

What do you mean by the rate of change of motion?

We know that every type of motion is not constant there is a possibility of changes in motion. The rate of change in motion can be defined as the rate of change in the velocity or speed of the object. This change in motion is due to any external force.

Rest and Motion

These are two states of a body at a point and at an instant of time. Both are simultaneous, rest and motion cannot occur together. If a body is at rest, it means there is motion and vice versa.

• Rest − Rest is a state of the body. When the body is fixed and not changing position concerning time and surroundings then we can say that body is at rest. When the body is at rest there is no velocity of change in motion. To check whether a body is at rest or in motion we have to consider a frame of reference.

• Motion − On the other hand, when a body is not at rest then the body is changing its position concerning time and the surrounding environment. However, the change in position is due to any external force, it can be artificial or natural. Also, the motion of the body has a particular rate of change and direction at an instant in time.

Properties of Moving Objects

When a body is in motion, it associates some extra characteristics then a body is at rest. Here are the following properties of moving objects

• A moving object has Kinetic energy

• A moving object has also a particular speed or direction of motion

• A moving object is also affected by some forces which act against the motion, such as Friction by surface and air.

• According to Relativity Theory, the mass of a body is also affected by motion.

What is Speed?

In simple words, speed is the rate of change in position when a body is moving. We can also say that the distance traveled by a moving body in a unit portion of time is the speed of that body.

By definition, the speed of a moving object is the length of the path traveled by that object in a unit interval of time. The speed is a scalar quantity means speed has only magnitude and no direction. The measurement unit of speed is a meter per second.

$$\mathrm{speed\:=\:\frac{distance\:traveled}{time}}$$

Types of speed

Speed can be classified into various types on the behalf of calculation and time factors. The major types of speed are the following.

• Uniform Speed − When the motion is uniform or we can say moving object traveling with a constant rate of changing in position then the speed is uniform.

• Non-Uniform Speed − The speed which is changing with time and path is known as non-uniform speed. Sometimes due to some reasons like traffic jams, destructive roads, etc., we change the gears of our vehicle so that motion is of non-uniform speed.

• Average speed − When we are traveling in a car with non-uniform speed then it is hard to describe the trip. So, we calculate all the speeds to measure the average time taken. Hence, when an object is moving at different speeds in different interval times then its average speed is

$$\mathrm{v_{a}\:=\:\frac{v_{1}t_{1}\:+\:v_{2}t_{2}\:+\:.....\:+\:v_{n}t_{n}}{t_{1}\:+\:t_{2}\:+\:t_{3}\:+\:......\:+\:t_{n}}}$$

If an object has a different speed but periods are equal then

$$\mathrm{v_{a}\:=\:\frac{v_{1}\:+\:v_{2}\:+\:.....\:+\:v_{n}}{n}}$$

• Instantaneous Speed − The speed of a moving object at an instant of time is called instantaneous speed. It is denoted by

$$\mathrm{v_{i}\:=\:\lim_{\Delta t\rightarrow 0}\:\frac{\Delta\:s}{\Delta\:t}}$$

• Relative Speed − It is the speed when we are considering a system of objects in which all the objects are in motion. The motion of an object may be in any direction. Thus, the speed of an object for other objects is called relative speed.

When two objects are approaching each other then

$$\mathrm{v_{r}\:=\:v_{1}\:+\:v_{2}}$$

When two objects are traveling in the same direction then

$$\mathrm{v_{r}\:=\:v_{1}\:-\:v_{2}}$$

Calculation of speed

Speed is a scalar quantity so we can operate all algebraic formulas in calculating it. Mostly, people use gadgets to determine the speed of a moving object. The device speedometer is used for measuring the speed of the object.

However, if we know about the distance and time then we can calculate the speed of an object by using the formula

$$\mathrm{speed\:=\:\frac{distance\:traveled}{time}}$$

We can use the standard measurement unit 𝑚𝑠−1.

Conclusion

In the above sections, we analyze all the concepts related to the motion of an object. Here, we learned that the change in motion is the change in speed of a moving particle which is known as acceleration. If the change in speed is negative then it is called de- acceleration.

Solved Example

1. A man run 400 m daily during morning walks. He takes 50 seconds to complete the circle of 400 m. calculate the speed of man.

Sol. Given that

The Distance traveled by man is 400 m and the time taken by man is 50 seconds. Thus,

$$\mathrm{speed\:=\:\frac{distance\:traveled}{time}}$$

$$\mathrm{speed\:=\:\frac{400\:m}{50\:sec}}$$

$$\mathrm{speed\:=8\:ms^{-1}}$$

FAQs

1. What is the dimensional formula for speed?

The dimensional formula for speed is $\mathrm{M^{0}\:L^{-1}\:T^{-1}}$

2. What is the difference between a scalar quantity and a vector quantity?

In science, quantities are classified into two forms, scalar, and vector. The main difference between both is that scalar quantity has no direction while vector quantity has a particular direction.

3. What is acceleration?

In simple words, we can say that the change in speed of a moving object is called acceleration. In general, people think that a fast-moving body is under acceleration but it is not necessary. Whether, the object is fast or slow but if there is no change in speed then there is no acceleration.

4. What is velocity?

Velocity is the rate of change of displacement with time. The velocity is a vector quantity.

5. What is the difference between speed and velocity?

The difference between speed and velocity are following.

• speed is scalar, velocity is a vector

• speed cannot be zero but velocity may be zero.

• speed cannot be negative but velocity can.