Speed and Velocity

Last Updated : 30 May, 2026

Speed and velocity are two important quantities used to describe the motion of an object. These quantities help in understanding how fast an object moves and, in the case of velocity, the direction of motion as well. Although both terms are often used interchangeably in daily life, they are scientifically different.

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Speed

Speed is defined as the rate at which an object covers distance with respect to time. It tells how fast an object is moving without considering its direction.

Mathematical Expression: \boxed {speed = \frac{\text{distance travelled}}{\text{time taken}} = \frac{d}{t}}

Characteristics of Speed

  • It is a scalar quantity
  • It has only magnitude and no direction
  • It is always positive or zero
  • It gives no information about the direction of motion
  • It depends on the total path travelled

Units and Dimensions

  • SI Unit: meter per second (m/s)
  • Other Units: km/h, cm/s
  • Dimensional Formula: M0L1T-1

Types of Speed

1. Average Speed

Average speed is defined as the ratio of the total distance travelled to the total time taken.It is useful when the speed of an object is not constant throughout its motion.

\boxed {\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}}

2. Instantaneous Speed

Instantaneous speed is the speed of an object at a particular instant of time. Mathematically, it is defined as the limit of average speed as the time interval approaches zero:

\boxed {v = \lim_{\Delta t \to 0} \frac{\Delta x}{\Delta t}}

  • It represents the reading shown by a speedometer
  • Always non-negative

Velocity

Velocity is defined as the rate at which displacement changes with respect to time. It describes both how fast an object is moving and in which direction.

Mathematical Expression: \boxed {\vec{v} = \frac{\Delta x}{\Delta t}}

Characteristics of Velocity

  • It is a vector quantity
  • It has both magnitude and direction
  • It can be positive, negative, or zero
  • It depends only on initial and final positions (displacement)
  • A change in velocity may occur due to change in magnitude, direction, or both

Units and Dimensions

  • SI Unit: meter per second (m/s)
  • Other Units: km/h, ft/s
  • Dimensional Formula: M0L1T-1

Types of Velocity

1. Average Velocity

Average velocity is defined as the total displacement of an object divided by the total time taken to produce that displacement.

\boxed {\text{Average Velocity} = \frac{\text{Total Displacement}}{\text{Total Time}}}

  • It gives the overall effect of motion
  • Direction is the same as displacement

2. Instantaneous Velocity

Instantaneous velocity is defined as the velocity of an object at a particular instant of time during its motion.

\boxed { \vec{v} = \frac{dx}{dt}}

  • It is obtained using calculus
  • Represents velocity at an exact moment
  • Its magnitude gives instantaneous speed

Relative Velocity

Relative velocity helps us understand how one object appears to move with respect to another. The velocity of one object as observed from another moving object is called relative velocity. If two objects A and B are moving with velocities vector (VA and VB) then the velocity of object A relative to object B is given by:

\boxed {\vec{V}_{AB} = \vec{V}_A - \vec{V}_B}

where:

  • VAB = velocity of A relative to B
  • VA, VB = velocities of A and B respectively
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Special Cases

1. Objects Moving in the Same Direction

When two objects move in the same direction, the relative velocity is equal to the difference of their velocities.

V_{AB} = |V_A - V_B|

In this case, the relative velocity decreases.

2. Objects Moving in Opposite Directions

When two objects move in opposite directions, the relative velocity is equal to the sum of their velocities.

V_{AB} = V_A + V_B

In this case, the relative velocity increases.

3. Objects Moving at an Angle

When two objects move at an angle with each other, relative velocity is calculated using vector addition or vector subtraction methods.

Do You Know?

  • Speed tells how fast an object moves
  • Velocity tells how fast and in which direction
  • An object can have constant speed but changing velocity (if direction changes)
  • If total displacement is zero, average velocity becomes zero, even if motion occurred

Solved Examples

Example 1. If a car goes a distance of 900 m in the west in 90 seconds. Find the speed and velocity of the car.

Solution: Here, 

Distance = 900 m

Time = 90 s

Speed = \frac{Distance}{Time}=\frac{900}{90}=10\ m/s

Velocity = 10 m/s to west

Example 2. If a car is moving with a. uniform speed covers a distance of 240 m in 6 seconds. Find the speed of the car and the time taken to cover a distance of 480 m.

Solution: Here,

Distance = 240 m

Time = 6 sec

Speed of car 'v' = ?

Time taken by car to cover 480 m distance 't' = ?

Speed = \frac{Distance}{Time}=\frac{240}{6}=40\ m/s

Time taken by the car to cover 480 m distance = \frac{Distance}{Speed}=\frac{480}{40}=12\ s             

Question 3. If a train travels from Delhi to Jaipur at the speed of 120 km/h and takes 3 hours to reach. Calculate the distance between the cities.

Solution: Here

Speed of the train 'v' = 120 km/h

Time taken 't' = 3 hours

We have to find the Distance 's' = ?

Distance = Speed × Time

= 120 × 3

= 360 km

Question 4. A boy throws a ball up in the air the ball rises about 50 m vertically in 2.5 seconds, then it comes back to the boy in the same position in another 2.5 seconds. Calculate

(i) Distance travelled

(ii) Displacement

(iii) Average Speed

(iv) Average Velocity

Solution: Here,

Distance travelled upwards = 50 m

Time taken = 2.5 seconds

(i) Total distance travelled = Distance travelled upward + Distance travelled downwards

= 50 + 50

= 100 m

(ii) Displacement = As the ball reaches to its initial point hence there will be zero displacement

= 0

(iii) Average Speed = \frac{Total\ Distance}{Total\ Time}= \frac{100}{5}=20\ m/s

(iv) Average velocity = 0 {As the displacement is 0 thus the velocity is also 0}.

Unsolved Problems

Problem 1. A car travels from Shimla to Chandigarh, covering a distance of 153 km in 4 hours. On its return journey from Chandigarh to Shimla, it takes 5 hours to cover the same distance. Calculate the average speed & average velocity of the car for the entire journey

Problem 2. If a train driver has a. reaction time of 0.4 s between seeing the obstacle applying the brakes. Assume the train is travelling at a speed of 72 km/h and the driver spots the obstacle calculate the distance travelled before applying the brakes.

Problem 3. Assume a ball moves with velocity v in the direction of the mirror and the mirror moves with velocity v in the direction of the ball,  So calculate the relative speed of the ball's image according to the ball?

Problem 4. A cyclist travels 12 km towards east in 30 minutes and then 8 km towards north in 20 minutes. Calculate the average speed and average velocity of the cyclist for the entire journey.

Problem 5. Two cars are moving on a straight road in opposite directions with speeds of 45 km/h and 55 km/h respectively. Calculate their relative velocity with respect to each other.

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Article Tags:
Physics
Physics-Class-11

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