# Average Speed and Average Velocity

## Difference and Examples of Average Speed and Average Velocity

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

Distance travelled – Distance travelled, as the name clearly tells, is the total distance travelled by the object.

Time taken – The time taken by the object to move the given distance.

Displacement – Displacement is the shortest distance between the initial point where the object was and the final point where the object ended up.

Speed – Speed is the distance travelled by an object in unit time. Speed is a scalar quantity. This means it has no specified direction. Speed refers to how fast an object is moving, or essentially the rate at which the distance is covered.

Velocity – Velocity is the total displacement of the object in a specified direction in unit time. Velocity is a vector quantity. This means it has a specified direction. Velocity refers to the time rate of displacement of the object. Imagine a person who walks for some distance before returning to his original position. Since velocity is the rate of displacement, this motion results in zero velocity. If a person wishes to maximise his velocity, he must maximise the displacement from his original position. Since velocity is a vector quantity, when evaluating it we must keep track of direction.

The main difference between speed and velocity is that speed does not take into account the direction since it is a scalar quantity, and speed depends upon distance travelled, while velocity is a vector quantity which takes into account the direction, and velocity depends upon displacement.

Average Speed:

The average speed of any object is the total distance travelled by that object divided by total time elapsed to cover the said distance. The average speed of an object tells you on an average rate at which it will cover 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 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:

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

Therefore, 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?

Distance = average speed(time)
Distance = 1.5(4) (60)
Distance = 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

Average Velocity:

Average velocity of an object can be defined as the displacement with regards to original position divided by the time. In other words, it is the rate at which an object makes displacements with time. Like average speed, the SI unit is meters per second. Average velocity can also have said to be the ratio of total displacement of an object to total time for this action to take place.

The direction of average velocity is the direction of displacement. Even if the speed of the object is fluctuating and its magnitude is changing, its direction would still be the same as the direction of displacement. The magnitude of average velocity is always either less than or equal to the average speed, because displacement is always less than or equal to the distance covered.

Average velocity is calculated by the formula V = D/t, where V equals the average velocity, D equals total displacement and t equals total time.

Problems:

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

Solution: V = D/t
V = (20 – 12)/ (5+3)
V = 8/8
V = 1 kilometre / minute

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

Solution: V = D/t
V = (10 -2.5)/2+1
V = 7.5/3
V = 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 x-axis?

Solution: Initial distance travelled by the person, x= 7 m,
Final distance travelled, xf = 18 m,
Initial time interval t= 4 s,
Final time interval t= 6 s,
Average velocity V = x− xf / t− t = 18−7 / 6−4 = 11 / 2 = 5.5 m/s.

The differences and similarities between Average Speed and Average Velocity:

Similarities – Both of these terms are average of some length by 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 only slight difference that in the first case, direction is to be mentioned.

Differences - Average speed is a scalar and is not affected by the presence or absence of a direction, while average velocity being a vector needs a direction. Average speed takes distance, that is total length travelled while being measured, while average velocity takes displacement, that is the straight distance from the original position to the final position.

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 go the 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 rectangle track with length = 50 meters and width = 20 meters. He travels around rectangle track twice, finally running back to 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.
Runs around 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 come 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 = Pi (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.