Average Speed And Average Velocity

Understanding the concepts of average speed and average velocity is essential in physics, especially when studying motion. While both terms are used to describe the movement of objects, they differ in key aspects. Average speed refers to the total distance travelled divided by the total time taken, offering a scalar quantity. In contrast, average velocity takes into account both the displacement and the direction, making it a vector quantity. Knowing the difference between these two concepts helps in accurately analysing the motion of objects in various situations. This page will explore the definitions, formulas, and real-life applications of average speed and average velocity to help you grasp these fundamental concepts in physics.

Distance and Displacement

Before understanding average speed and average velocity, we must first understand the distinction between distance and displacement. The scalar quantity "distance" represents how much ground an object has covered. The shortest distance between two points is represented by displacement, which is a vector quantity. If a particle moves in a circle, for example, the distance travelled after one revolution equals the circumference of the circle, but the displacement is zero.

Let's have a look at the definitions of speed and velocity.

Speed and Velocity

Speed is a scalar quantity that refers to how fast an object moves. It is the distance traveled per unit of time, regardless of the direction of movement. The formula for speed is:

Speed = Total Distance / Total Time

Speed is usually measured in units like meters per second (m/s) or kilometers per hour (km/h). Since speed does not consider direction, it simply tells us how much ground an object has covered during its motion.

Velocity is a vector quantity that refers to the rate of change of an object's position in a specific direction. Unlike speed, velocity not only considers how fast an object is moving but also the direction of its motion. The formula for velocity is:

Velocity = Displacement / Time

Velocity is typically measured in meters per second (m/s), and the direction of movement is an essential aspect of its calculation. A change in direction, even at the same speed, will result in a change in velocity.

Average Speed and Average Velocity

Average Speed

Average speed is a scalar quantity that represents the total distance traveled divided by the total time taken. It does not take direction into account, focusing solely on how fast an object moves over a given period. The formula for average speed is:

Average Speed = Total Distance / Total Time

Example: If a car travels 100 km in 2 hours, the average speed is:

Average Speed = 100 km / 2 hours = 50 km/h

Average Velocity

Average velocity is a vector quantity that accounts for both the displacement (change in position) and the direction of motion. It is calculated as the total displacement divided by the total time taken. Unlike speed, average velocity considers the straight-line distance between the starting and ending points, not the total path traveled.

The formula for average velocity is:

Average Velocity = Displacement / Total Time

Example: If a person travels 100 km to the east in 2 hours, the average velocity is:

Average Velocity = 100 km (East) / 2 hours = 50 km/h East

Difference Between Average Velocity and Average Speed

The difference between Average Speed and Average Velocity are given by

To know about average speed and average velocity, first, we must know of some terms and their meanings.

The formula for Average Speed and Average Velocity 

If ‘Δx’ is the displacement of an object in time ‘Δt’, then:

The formula for average speed is given as:

vav  = Δx/Δt

You noticed that the formula for average velocity and average speed is the same.

The only difference lies in the type of physical quantity, i.e., speed and velocity. Speed is a scalar quantity that has magnitude only. However, velocity is a vector quantity that has both magnitude and direction.

Now, let us go through some average speed problems:

Problems on Average Speed

1. A car travels a distance of 70 km in 2 hours. What is the average speed?

Answer: average speed = distance/time

Therefore, the average speed of the car is 70 km/2 hours = 35km/hour.

2. A person can walk at a speed of 1.5 meters/second. How far will he walk in 4 minutes?

Answer: average speed = distance/time

Distance = average speed(time)

= 1.5(4) (60) = 360 meters

3. A train travels in a straight line at a constant speed of 60 km/h for a particular distance d and then travels another distance equal to 2d in the same direction at a constant speed of 80 km/h in the same direction as it was previously going.  a) What is the average speed of the train during the whole journey?

Solution:  a) The time t1 to cover distance d at a speed of 60 km/h is given by t1 = d / 60

The time t2 to cover distance 2d at a speed of 80 km/h is given by t2 = 2d / 80

Average Speed = distance/time = (d + 2d) / (d/60) + (2d/80) 

= 3d / (80d + 2d × 60)/(60 × 80)

= 3 d/(200d/4800) = 3d (4800)/200d = 72 km/h

4. Calculate the average velocity at a particular time interval of a person if he moves 7 m in 4 s and 18 m in 6 s along the x-axis?

Solution: Initial distance travelled by the person, xi = 7 m,

Final distance travelled, xf  = 18 m,

Initial time interval ti = 4 s,

Final time interval tf = 6 s,

Average velocity v = xi − xf / ti − tf   = 18 − 7 / 6 − 4 = 11 / 2 = 5.5 m/s.

From the above text, we understand that the average speed of any object is the total distance travelled by that object divided by the total time elapsed to cover the said distance. 

The average speed of an object tells you an average rate at which it will cover the distance; that is, an object has a speed of 30km/hour, its position will change on an average by 30km each hour. Average speed is a rate that is a quantity divided by the time taken to get that quantity. SI unit of speed is meters per second.

Average speed is calculated by the formula S = d/t, where S equals the average speed, d equals total distance and t equals total time.

Problems on Average Velocity

1. A truck driver drives 20 km down the road in 5 minutes. He then reverses and drives 12 km down the road in 3 mins. What is his average velocity?

Solution: v = D/t

v = (20 - 12)/(5 + 3)

= 8/8 = 1 kilometre/minute

2. A man walks 10 km east in 2 hours and then 2.5 km west in 1 hour. Calculate the total average velocity of a man?

Solution: vav = D/t

= (10  - 2.5)/2 + 1

= 7.5/3

vav = 2.5 km/hr

3. Calculate the average velocity at a particular time interval of a person if he moves 7 m in 4 s and 18 m in 6 s along the x-axis?

Solution: Initial distance travelled by the person, xi = 7 m,

Final distance travelled, xf = 18 m,

Initial time interval ti = 4 s,

Final time interval tf = 6 s,

Average velocity vav = xi − xf / ti − tf  

= 18 /(6 − 4) = 11/2 = 5.5 m/s

The Similarities Between Average Speed and Average Velocity

Similarities – Both of these terms are average of some length by the time taken. The SI unit and other standard units of measurement of both average speed and average velocity are the same. The formula used to calculate the average speed and average velocity is virtually the same, v = D/t, s = d/t, with the only slight difference that in the first case direction is to be mentioned.

Problems Related to Both Average Speed and Average Velocity

1. A car travels along a straight road to the east for 120 meters in 5 seconds, then goes west for 60 meters in 1 second. Determine average speed and average velocity.

Solution:

Distance = 120 meters + 60 meters = 180 meters

Displacement = 120 meters – 60 meters = 60 meters, to east.

Time elapsed = 5 seconds + 1 second = 6 seconds.

Average speed = Distance / time elapsed = 180 meters / 6 seconds = 30 meters/second.

Average velocity = Displacement / time elapsed = 60 meters / 6 seconds = 10 meters/second.

2. A runner is running around a rectangle track with length = 50 meters and width = 20 meters. He travels around the rectangle track twice, finally running back to the starting point. If the total time he takes to run around the track is 100 seconds, determine average speed and average velocity.

Solution:

The circumference of the rectangle, which is the distance travelled in one round = 2(50 meters) + 2(20 meters) = 100 meters + 40 meters = 140 meters.

When a runner runs around the rectangle twice = 2(140 meters) = 280 meters.

Distance = 280 meter

Displacement = 0 meter. (Since the runner came back to initial point)

Average speed is equal to the distance / time elapsed = 280 meters/100 seconds = 2.8 meters/second.

Average velocity is equal to the displacement / time elapsed = 0/100 seconds = 0

3. A man starts walking from a point on a circular field of radius 0.5 km and 1 hour later he finds himself at the same point where he initially started. 

a) What is the average speed for the whole journey he travelled? What is the average velocity of this man for the same?

Solution: a) If this man walks around a circular field and comes back to the same point, he has covered a distance which is equal to the circumference of the circle.

Thus, average speed he travelled = Distance/time = circumference time = π (0.5) (2)/1 hour = 3.14 km/hour (approximately).

b) If he walks around in a circle and comes back to the same point where he started in a circle then the change in his position is zero. Since the change in his position is zero, displacement is also equal to zero. This means the average velocity is also equal to zero.