Understanding Average Speed and Average Velocity: Formula, Definition, and Examples
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.
FAQs on Average Speed And Average Velocity
1. What is the main difference between average speed and average velocity according to the CBSE Class 11 Physics syllabus?
The main difference is that average speed is a scalar quantity calculated as total distance travelled divided by total time taken, while average velocity is a vector quantity that measures total displacement divided by the total time taken, considering direction. Thus, average speed only measures magnitude, whereas average velocity includes both magnitude and direction.
2. How can you effectively calculate average velocity for journeys with changes in direction?
To calculate average velocity in situations involving changes in direction, determine the net displacement (shortest straight-line distance from initial to final position) and divide it by the total time taken. Displacement sums any movements back towards the starting point, which can reduce the value of average velocity compared to average speed.
3. What key steps are involved in solving a typical average speed question for board exams?
Follow these steps while solving:
- Identify all segments of the journey and their individual distances and time intervals.
- Add up the total distance travelled.
- Calculate the total time taken covering all segments.
- Apply the formula: Average Speed = Total Distance / Total Time.
4. Why can the average velocity of a round trip be zero even if the average speed is not?
The average velocity is zero when the displacement is zero, such as in a round trip where the ending point is the same as the starting point. Even though the object may have covered a significant distance (hence, nonzero average speed), the straight-line displacement is zero, resulting in zero average velocity.
5. In what type of motion do average speed and average velocity have equal magnitudes, and why?
Average speed and average velocity are equal when an object moves in a straight line without changing direction. In this scenario, total distance and displacement have the same value, so both quantities yield the same numerical answer.
6. How does the path taken by an object affect the relationship between average speed and average velocity?
If the path of the object is not a straight line (it curves or loops), the average speed will usually be higher than the average velocity. This is because distance (used for speed) is always equal to or greater than displacement (used for velocity), especially for non-linear paths.
7. Can you list the standard units used for expressing average speed and average velocity in NCERT Physics?
Both average speed and average velocity are most commonly expressed in meters per second (m/s) in SI units. Other accepted units include kilometers per hour (km/h) and centimeters per second (cm/s), according to the context of the question.
8. What mistakes should be avoided when answering calculation questions on average speed and average velocity in board exams?
Common mistakes include:
- Confusing total distance with displacement.
- Omitting direction when writing velocity answers.
- Not converting all time and distance units to a consistent system.
- Failing to show stepwise working, which can lead to loss of marks as per CBSE marking scheme.
9. What happens to the ratio of average speed to average velocity when the motion involves a return to the starting point?
When an object returns to its starting point, the average velocity becomes zero (displacement is zero), whereas average speed remains positive due to the total distance travelled. In this case, the ratio of average speed to average velocity is undefined or considered to be infinitely large.
10. How can understanding the concept of average velocity help in analysing real-life scenarios like running or driving?
Knowledge of average velocity helps evaluate the efficiency of movement in a given direction, especially when the actual path may include turns or returns. In real-life cases like running laps or driving, average velocity indicates progress towards the destination, while average speed shows the pace of covering ground. This distinction is useful for route planning and time management.
