Measuring the Rate of Motion

Discover how we measure speed and velocity, understand the difference between them, and learn to calculate average speed in various scenarios!

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Cricket Bowling Speed
143 km/h
This means the cricket ball travels at a rate of 143 kilometers per hour. It tells us how fast the ball is moving through the air.
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Speed Limit Sign
60 km/h
This signboard indicates the maximum allowed speed for vehicles on this road. It's a safety measure to control the rate of motion.
Speed Formula
v = s/t
Where:
v = speed (m/s)
s = distance (m)
t = time (s)

Average Speed = Total Distance ÷ Total Time
Speed Calculator
Enter distance and time to calculate speed
Speed
🏃‍♂️
  • Definition: Rate of motion (how fast)
  • Nature: Scalar quantity
  • Direction: Not specified
  • Unit: m/s, km/h
  • Value: Always positive
  • Example: Car moving at 60 km/h
Velocity
🧭
  • Definition: Speed with direction
  • Nature: Vector quantity
  • Direction: Must be specified
  • Unit: m/s, km/h
  • Value: Can be positive or negative
  • Example: Car moving at 60 km/h north
NCERT Examples - Click Any Example to Start
← Click indicators below or use Previous/Next buttons - Each example will narrate from the beginning →
Example 7.1: Average Speed Calculation
Problem: An object travels 16 m in 4 s and then another 16 m in 2 s. What is the average speed of the object?
Average Speed = Total Distance ÷ Total Time
📋 Solution Approach:
  1. Calculate total distance traveled
  2. Calculate total time taken
  3. Apply average speed formula
  4. Verify the result
16 m 16 m 4 s 2 s Total Distance = 32 m Total Time = 6 s Average Speed = 5.33 m/s
Step 1: Identify the given information
First segment: s₁ = 16 m, t₁ = 4 s
Second segment: s₂ = 16 m, t₂ = 2 s
We need to find the average speed for the entire journey. Average speed considers the total distance and total time.
Step 2: Calculate the total distance
s_total = s₁ + s₂
s_total = 16 m + 16 m = 32 m
The total distance is the sum of all distances covered, regardless of direction.
Step 3: Calculate the total time
t_total = t₁ + t₂
t_total = 4 s + 2 s = 6 s
The total time is the sum of all time intervals during the journey.
Step 4: Apply the average speed formula
v_average = s_total ÷ t_total
v_average = 32 m ÷ 6 s = 5.33 m/s
The average speed is calculated by dividing the total distance by the total time taken.
Average speed = 5.33 m/s
Key Insight: The object traveled at different speeds during the two segments:
  • First segment speed: 16 m ÷ 4 s = 4 m/s
  • Second segment speed: 16 m ÷ 2 s = 8 m/s
But the average speed (5.33 m/s) is not the simple average of these two speeds. It must be calculated using the total distance and total time. This demonstrates why we can't simply average the individual speeds to find average speed.
Example 7.2: Speed Unit Conversion
Problem: The odometer of a car reads 2000 km at the start and 2400 km at the end of a trip. If the trip took 8 h, calculate the average speed in km/h and m/s.
Average Speed = Distance ÷ Time
1 km/h = (1000 m) ÷ (3600 s) = 0.278 m/s
📋 Solution Approach:
  1. Find distance from odometer readings
  2. Calculate speed in km/h
  3. Convert km/h to m/s
  4. Verify unit conversion
2000 km 2400 km 🚗 Distance = 400 km Time = 8 h 50 km/h = 13.9 m/s
Step 1: Identify the given information
Initial odometer reading = 2000 km
Final odometer reading = 2400 km
Time taken = 8 h
The odometer records the total distance traveled by the car. We need to find the average speed in both km/h and m/s.
Step 2: Calculate the distance traveled
Distance = Final reading - Initial reading
Distance = 2400 km - 2000 km = 400 km
The distance traveled is the difference between the final and initial odometer readings.
Step 3: Calculate the average speed in km/h
Average speed = Distance ÷ Time
Average speed = 400 km ÷ 8 h = 50 km/h
The average speed is the total distance divided by the total time taken.
Step 4: Convert km/h to m/s
1 km/h = (1000 m) ÷ (3600 s) = 0.278 m/s
50 km/h = 50 × 0.278 = 13.9 m/s
To convert from km/h to m/s, we multiply by 1000 (to convert km to m) and divide by 3600 (to convert h to s). This is equivalent to multiplying by the conversion factor 0.278.
Average speed = 50 km/h = 13.9 m/s
Key Insight: Unit conversion is essential in physics to express quantities in the appropriate units for different contexts.
  • km/h is commonly used for vehicle speeds in everyday life
  • m/s is the SI unit of speed used in scientific calculations
  • The conversion factor (0.278) can be derived from dimensional analysis:
    1 km/h = (1 km)/(1 h) = (1000 m)/(3600 s) = 0.278 m/s
Always check your units when solving physics problems to ensure consistency and avoid errors.
Example 7.3: Speed vs. Velocity
Problem: Usha swims in a 90 m long pool. She covers 180 m in one minute by swimming from one end to the other and back. Find her average speed and average velocity.
Average Speed = Total Distance ÷ Time
Average Velocity = Displacement ÷ Time
📋 Solution Approach:
  1. Calculate total distance traveled
  2. Find displacement (final - initial position)
  3. Calculate average speed using distance
  4. Calculate average velocity using displacement
Total Distance = 180 m Displacement = 0 m 🏊‍♀️ Start/End Speed = 3 m/s, Velocity = 0 m/s
Step 1: Identify the given information
Pool length = 90 m
Total distance covered = 90 m + 90 m = 180 m
Time taken = 1 min = 60 s
Usha swims from one end to the other and back, covering the pool length twice.
Step 2: Calculate the displacement
Initial position = Starting point of the pool
Final position = Starting point of the pool (after returning)
Displacement = Final position - Initial position = 0 m
Displacement is a vector quantity that measures the straight-line distance and direction from the initial to the final position. Since Usha returns to her starting point, her displacement is zero.
Step 3: Calculate the average speed
Average speed = Total distance ÷ Time
Average speed = 180 m ÷ 60 s = 3 m/s
Average speed is a scalar quantity that considers only the magnitude of the total distance traveled, regardless of direction.
Step 4: Calculate the average velocity
Average velocity = Displacement ÷ Time
Average velocity = 0 m ÷ 60 s = 0 m/s
Average velocity is a vector quantity that depends on displacement. Even though Usha was moving the entire time, her average velocity is zero because her displacement is zero.
Average speed = 3 m/s, Average velocity = 0 m/s
Key Insight: This example perfectly illustrates the fundamental difference between speed and velocity:
  • Speed (scalar): Depends on total distance traveled (180 m)
  • Velocity (vector): Depends on displacement (0 m)
If we had measured Usha's instantaneous velocity at different points during her swim, it would have been:
  • First half: Positive velocity (moving away from start)
  • Second half: Negative velocity (moving toward start)
But the average over the entire journey is zero because the positive and negative components cancel out.
km/h to m/s Conversion
50 km/h
↓
50 × (1000 m / 1 km)
↓
50 × (1 h / 3600 s)
↓
50 × (1000/3600) = 13.9 m/s
Quick Conversion Formula
km/h × 5/18 = m/s
m/s × 18/5 = km/h
Example: 72 km/h to m/s
↓
72 × (5/18) = 20 m/s

NCERT Activities

Activity 7.6: Walking Speed
  • Measure the time it takes you to walk from your house to your bus stop or school
  • Consider that your average walking speed is 4 km/h
  • Estimate the distance of the bus stop or school from your house
Formula: Distance = Speed × Time
If time = 15 minutes = 0.25 h
Distance = 4 km/h × 0.25 h = 1 km
Activity 7.7: Thunder and Lightning
  • During cloudy weather, observe thunder and lightning
  • Sound of thunder takes time to reach you after seeing lightning
  • Measure this time interval using a stopwatch
  • Calculate the distance of lightning (Speed of sound = 346 m/s)
Formula: Distance = Speed × Time
If time delay = 3 seconds
Distance = 346 m/s × 3 s = 1038 m ≈ 1 km

Practice Questions

Q1.
Distinguish between speed and velocity.
Answer:
Speed: Rate of motion, scalar quantity, only magnitude, always positive
Velocity: Speed with direction, vector quantity, has magnitude and direction, can be positive or negative
Q2.
Under what condition(s) is the magnitude of average velocity of an object equal to its average speed?
Answer: The magnitude of average velocity equals average speed when the object moves in a straight line without changing direction. In this case, displacement equals distance travelled.
Q3.
What does the odometer of an automobile measure?
Answer: An odometer measures the total distance travelled by the automobile. It does not measure displacement, only the actual path length covered.
Q4.
What does the path of an object look like when it is in uniform motion?
Answer: When an object is in uniform motion, its path is a straight line. The object covers equal distances in equal intervals of time along this straight path.
Q5.
During an experiment, a signal from a spaceship reached the ground station in five minutes. What was the distance of the spaceship from the ground station? (Speed of light = 3 × 10⁸ m/s)
Solution:
Given: Time = 5 minutes = 300 s, Speed = 3 × 10⁸ m/s
Distance = Speed × Time
Distance = 3 × 10⁸ × 300 = 9 × 10¹⁰ m
Answer: 9 × 10¹⁰ meters
Explore Rate of Motion
Understanding Speed
Speed is the rate at which objects move. It tells us how fast an object is moving by measuring the distance travelled in unit time. Different objects can move at different rates - some fast, some slow.
Speed = Distance ÷ Time
SI Unit: metre per second (m/s)
Other Units: km/h, cm/s
Average Speed: Total distance ÷ Total time
Speed
• Scalar quantity (only magnitude)
• Always positive
• No direction specified
• Example: 60 km/h
Velocity
• Vector quantity (magnitude + direction)
• Can be positive or negative
• Direction must be specified
• Example: 60 km/h north
Key Points to Remember
• Speed is always positive, velocity can be positive or negative
• Average velocity = (Initial velocity + Final velocity) ÷ 2 (for uniform acceleration)
• When an object returns to its starting point, displacement = 0, so average velocity = 0
• Odometer measures distance, not displacement
• To convert km/h to m/s: multiply by 5/18
• To convert m/s to km/h: multiply by 18/5