Average Speed and Average Velocity
Average speed and average velocity-The The speed is defined as the distance per unit time and average speed is defined as total distance covered in per unit of total time or the average rate of covering the total distance. The relationship between total distance, time and average speed is, the total distance is the product of total time taken and average speed. The average speed is the total distance covered per unit time and the average velocity is total displacement covered in per unit time is known as average velocity. The average velocity and average speed both are very important in Dynamics or Kinematics in the calculation of net energy. Before we study in detail what is average speed and average velocity, we are needed to study first what are distance and displacement.
Distance. The total distance covered by an object during its journey is known as distance. The distance is a scalar quantity since it is represented by a magnitude only. The S.I unit of distance is meter.
Displacement. The shortest distance between the initial and final position of an object during its journey is known as displacement. Displacement is the vector quantity since it represented by direction and magnitude. The S.I unit of displacement is meter.
Example. Mohan went 12 km west from his house and then turned 5 km towards the north, show the displacement and the distance covered by him.
The distance covered covered by Mohan is = 12 + 5 =17 km
The displacement is = shortest distance = AC
Triangle ΔABC is the right triangle in which ∠B is the right angle
The displacement covered by Mohan = 13 km
When anything changes its position with respect to time then we say that the thing is in motion. According to the state of motions, it is of two kinds (i) Uniform Motion (ii) Non-Uniform Motion.
(i) Uniform Motion
- A moving car on a busy road.
- A Boy running in the field
(ii) Non-Uniform Motion.
- Moving fan
- Moon around the earth
Distance. The distance is the total distance covered by an object during its travel in a given time.
Displacement. The shortest distance covered by an object during the travel, in other words, the minimum distance from the initial point and final point during the journey of an object.
Average Speed. Per unit of the total distance covered in per unit of the total time is known as average speed.
Average Velocity. Per unit of the total displacement covered in per unit, time is known as average velocity.
Example. Rohit traveled a distance of 24 km through a bicycle in 1 hour and then turned right and traveled 7 km in 10 minutes, find the average velocity and average speed of the bicycle he is cycling.
The total distance covered is = 24 + 7 = 31 km
Total time taken = 1 hour + 10 minutes
Therefore average speed is = 26.57 km/h
Total displacement = shortest distance in journey = BC
Total displacement = 25 km
Total time is taken = 7/6 Hr
Hence the average velocity of the bicycle is 21.43 km/h
Example. Ramaswami Lingham went to his school with an average velocity of 6 km/h and returned to his home at an average speed of 8 km/h, find his average speed in his journey?
Solution. Let the distance from his home to school is = x km
His speed from home to school = 6 km/h
Time is taken by him from home to school = x/6
Distance from school to home = x km
His speed from school to home = 8 km/h
Time is taken by him from school to home = x/8
Total time taken in total journey = x/6 + x/8 = 7x/24
∴ The total distance he covered = x + x = 2x km
Therefore the average speed of Ramswami Lingam is 6.86 km/h.
Example. Shyam makes a round of a circular ground in 5 minutes if the radius of the ground is 350 m, find how much distance, displacement, he will cover in 12.5 minutes?
Solution. Distance covered by Shyam in one round of the ground = circumference of the ground = 2πr
Where r is the radius of the ground which is given to us = 350 m
Distance covered in one round = 2 × (22/7) × 350 = 2200 m
Time is taken to cover one round = 5 minutes
Speed = 440 meter/min
Time is given = 12.5 min.
Distance = Speed × Time = 440 × 12.5 = 5500 meter = 5.5 km
In 5 minutes Shyam covers → 1 round
In 1 minute he will cover → 1/5 round
In 12.5 minutes he will cover → 12.5 × 1/5 = 2.5 round
Suppose Shyam starts to move from A then after 2.5 round his position will be at B
The displacement = AB = Diameter of the ground = 400 meter