Telangana Project

1. Speed:

Definition: Speed is the rate at which an object covers distance.
Nature: It is a scalar quantity, meaning it has only magnitude and no direction.
Formula:
$Speed = \frac{Distance}{Time}$
SI Unit: Meter per second ( $m/s$ ).
Types of Speed:
- Uniform Speed: When an object covers equal distances in equal intervals of time.
- Variable Speed: When an object covers unequal distances in equal intervals of time.
- Average Speed: Total distance traveled divided by total time taken.
  $Average Speed = \frac{Total Distance}{Total Time}$

2. Velocity:

Definition: Velocity is the rate of change of displacement.
Nature: It is a vector quantity, meaning it has both magnitude and direction.
Formula:
$Velocity = \frac{Displacement}{Time}$
SI Unit: Meter per second ( $m/s$ ).
Types of Velocity:
- Uniform Velocity: When an object covers equal displacements in equal intervals of time.
- Variable Velocity: When the magnitude or direction of velocity changes.
- Average Velocity: Total displacement divided by total time taken.
  $Average Velocity = \frac{Total Displacement}{Total Time}$

3. Differences Between Speed and Velocity:

Aspect	Speed	Velocity
Nature	Scalar (only magnitude)	Vector (magnitude + direction)
Dependency	Depends on distance	Depends on displacement
Sign	Always positive or zero	Can be positive, negative, or zero
Example	A car travels 60 km in 1 hour	A car moves 60 km north in 1 hour

Speed: Rate of distance covered; scalar; $m/s$ .
Velocity: Rate of displacement; vector; $m/s$ .
Speed ≥ Magnitude of Velocity.
If motion is along a straight line without changing direction, Speed = Magnitude of Velocity.

Q1: A car travels 100 km in 2 hours. What is its average speed?
A1:

Q2: A person walks 6 km east in 2 hours and then 8 km west in 2 hours. What is the average velocity?
A2:

Total Displacement = 6 km (east) − 8 km (west) = −2 km (west).
Total Time = 2 + 2 = 4 hours.
Average Velocity = $\frac{Total Displacement}{Total Time} = \frac{- 2}{4} = - 0.5 km/h$ .
Magnitude = 0.5 km/h, Direction = West.

Q3: A cyclist covers 12 km in 2 hours. What is the uniform speed?
A3:

Q4: A train moves 150 km north in 3 hours and then 100 km south in 2 hours. What is the average velocity?
A4:

Total Displacement = 150 km (north) − 100 km (south) = 50 km (north).
Total Time = 3 + 2 = 5 hours.
Average Velocity = $\frac{Total Displacement}{Total Time} = \frac{50}{5} = 10 km/h$ .
Direction = North.

Q5: A runner completes one lap of a circular track of radius 70 m in 2 minutes. What are the average speed and average velocity?
A5:

Circumference of the track = $2 𝜋 𝑟 = 2 \times \frac{22}{7} \times 70 = 440 m$ .
Total Distance = 440 m.
Total Displacement = 0 (as the runner returns to the starting point).
Total Time = 2 minutes = 120 seconds.
Average Speed = $\frac{Total Distance}{Total Time} = \frac{440}{120} = 3.67 m/s$ .
Average Velocity = $\frac{Total Displacement}{Total Time} = \frac{0}{120} = 0 m/s$ .

Q1: A bus travels 90 km in 1.5 hours. What is its average speed?
A1:

Average Speed = $\frac{Total Distance}{Total Time} = \frac{90}{1.5} = 60 km/h$ .

Q2: A man walks 12 km east in 3 hours and then 5 km west in 1 hour. What is the average velocity?
A2:

Total Displacement = 12 km (east) − 5 km (west) = 7 km (east).
Total Time = 3 + 1 = 4 hours.
Average Velocity = $\frac{Total Displacement}{Total Time} = \frac{7}{4} = 1.75 km/h$ .
Direction = East.

Q3: A car moves with a uniform speed of 20 m/s for 10 seconds. What is the distance covered?
A3:

Q4: A particle moves 20 m north in 4 seconds and then 15 m south in 3 seconds. What is the average velocity?
A4:

Total Displacement = 20 m (north) − 15 m (south) = 5 m (north).
Total Time = 4 + 3 = 7 seconds.
Average Velocity = $\frac{Total Displacement}{Total Time} = \frac{5}{7} = 0.71 m/s$ .
Direction = North.

Q5: A boy runs along a circular track of radius 35 m and completes one lap in 70 seconds. What are the average speed and average velocity?
A5:

Circumference of the track = $2 𝜋 𝑟 = 2 \times \frac{22}{7} \times 35 = 220 m$ .
Total Distance = 220 m.
Total Displacement = 0 (as the boy returns to the starting point).
Total Time = 70 seconds.
Average Speed = $\frac{Total Distance}{Total Time} = \frac{220}{70} = 3.14 m/s$ .
Average Velocity = $\frac{Total Displacement}{Total Time} = \frac{0}{70} = 0 m/s$ .

Unit 2.2 – Speed & Velocity