Motion in One Dimension-

Before you go through this article, make sure that you have gone through the previous article on Motion in One Dimension.

We have discussed-

• In one-dimensional motion, particle moves along a straight line.
• It is also known as rectilinear motion.

Various parameters related to motion are-

Speed-

 Rate of change of distance of a particle is called as its speed. OR Distance covered by a particle per unit time is called as its speed.

Mathematically,

Example-

Consider-

• A particle moves in a circular path of radius 7 m.
• It starts its journey from point A and ends at the same point in time 11 seconds.

Then, Speed of the particle

= Distance covered by the particle during its motion / Time taken

= Circumference of the circle / Time taken

= (2 x 22/7 x 7) / 11

= 4 m/s

Characteristics-

The characteristics of speed are-

• It is a scalar quantity.
• Speed is always positive. It can never be negative.
• Speed can increase or decrease with time.
• Speed is never zero for a moving particle.
• The SI unit of speed is meter per second (m/s).
• The dimensional formula of speed is [M0L1T-1].

Types of Speeds-

There are mainly following four types of speeds-

1. Uniform Speed
2. Variable Speed
3. Average Speed
4. Instantaneous Speed

1. Uniform Speed-

 A particle is said to be moving with uniform speed if it covers equal distances in equal intervals of time. OR A particle is said to be moving with uniform speed if it moves continuously with constant speed.

It is worth remembering-

The direction of motion of the particle may change while moving with constant speed.

2. Variable Speed-

 A particle is said to be moving with variable speed if it covers equal distances in unequal intervals of time or unequal distances in equal intervals of time.

3. Average Speed-

 The average speed of a particle is that constant speed with which the particle covers the same distance in a given time as it does while moving with variable speed during the given time.

Mathematically,

It is the ratio of total distance travelled by the particle to the total time taken in which the distance is travelled.

If Δx is the distance travelled by particle in time Δt, then average speed is given by-

4. Instantaneous Speed-

 Instantaneous speed is the speed of particle at a particular instant of time.

Mathematically,

Instantaneous speed is the limiting value of average speed as the time interval becomes infinitesimally small.

If  Δx is the distance covered by a particle in the time interval Δt, then-

Velocity-

 Rate of change of displacement of a particle is called as its velocity. OR Rate of change of position vector of a particle is called as its velocity.

Mathematically,

Its direction is same as that of displacement.

Example-

Consider-

• A particle moves in a circular path of radius 7 m.
• It starts its journey from point A and ends at the same point in time 11 seconds.

Velocity of the particle

= Displacement of the particle / Time taken

= 0 / 11

= 0 m/s

Characteristics-

The characteristics of velocity are-

• It is a vector quantity.
• Velocity can be positive, negative or zero.
• Velocity can increase or decrease with time.
• Velocity may be zero for a moving particle.
• The SI unit of velocity is meter per second (m/s).
• The dimensional formula of velocity is [M0L1T-1].

Types of Velocities-

There are mainly following four types of velocities-

1. Uniform Velocity
2. Variable Velocity
3. Average Velocity
4. Instantaneous Velocity

1. Uniform Velocity-

 A particle is said to be moving with uniform velocity if it covers equal displacements in equal intervals of time. OR A particle is said to be moving with uniform velocity if it moves continuously in the same direction with constant speed.

It is worth remembering-

2. Variable Velocity-

 A particle is said to be moving with variable velocity if it covers equal displacements in unequal intervals of time or unequal displacements in equal intervals of time. OR A particle is said to be moving with variable velocity if either magnitude of velocity or direction or both changes during its motion.

3. Average Velocity-

 The average velocity of a particle is that constant velocity with which the particle undergoes same displacement in a given time as it undergoes while moving with variable velocity during the given time.

Mathematically,

It is the ratio of total displacement of the particle to the total time interval in which the displacement occurs.

Consider-

• At any time t1, the position vector of the particle is $\overrightarrow{r1}$.
• At time t2, the position vector is $\overrightarrow{r2}$.

Then for this interval, average velocity is given by-

4. Instantaneous Velocity-

 Instantaneous speed is the velocity of particle at a particular instant of time.

Mathematically,

Instantaneous velocity is the limiting value of average velocity as the time interval becomes infinitesimally small.

If  Δr is the displacement of particle in the time interval Δt, then-

Difference Between Speed And Velocity-

Some important differences between speed and velocity are-

 Speed Velocity Rate of change of distance of a particle is called as its speed. Rate of change of displacement of a particle is called as its velocity. It is a scalar quantity. It is a vector quantity. Speed is either positive or zero. It can never be negative. Velocity can be positive, negative or zero. Speed is never zero for a moving particle. Velocity can be zero for a moving particle. Speed tells nothing about the direction of motion of the particle. Velocity tell the direction of motion of the body.

Important Points-

It is important to note the following points-

Point-01:

According to convention,

• If the particle moves upwards or towards right, its velocity is taken positive.
• If the particle moves downwards or towards left, its velocity is taken negative.

Point-02:

Velocity tell the direction of motion of the particle as-

• If the velocity is positive, particle must be moving towards positive direction.
• If the velocity is negative, particle must be moving towards negative direction.

Point-03:

• If motion takes place in the same direction, then average speed and average velocity are same.
• This is because distance and displacement are then same.

Point-04:

• The magnitude of instantaneous velocity is always instantaneous speed.
• Instantaneous speed and instantaneous velocity differs only by direction.
• However, magnitude of average velocity is not always average speed.
• Speedometer of an automobile measures instantaneous speed of the automobile.

To gain better understanding about Speed and Velocity,

Watch this Video Lecture

Next Article- Acceleration and Retardation

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