Table of contents  
Slow or Fast  
Speed  
Types of Motion  
Measurement of Time  
DistanceTime Graph 
We can determine whether an object is fast or slow by determining its speed.
The distance covered by an object in unit time is called the speed of the object.
The mathematical expression for speed is given by:
The SI unit of speed is meter/sec (m/s). 
Example: In a 4000 m marathon race, Roger covers 400 meters in 1 minute. What is the speed of Roger in m/s and in km/h respectively?
Sol: (i) The speed of Roger in m/s
Roger covers 400 m distance in 1 min
We know, 1 min = 60 sec [Converting minutes to seconds]
The speed of Roger is 6.66 m/s
(ii) Now, we have to find the speed of Roger in km/h.
To do so, first, we must convert meters to kilometers and then time in seconds to time in an hour.
We know, 1 km = 1000 m
⇒ 1m =km
⇒= 0.4 km [Distance covered by Roger in 1 minute]
1 hour = 60 minutes
∴ 1 min =
Now, the speed of Roger in km/h is
Speed =
Speed = 0.4 x 60
Speed = 24 km/h
Tip: To convert speed from km/h to m/s multiply it by 5/18 and to convert it from m/s to km/s multiply it by 18/5.
[Question: 982788]
Example: Manish covers the distance from his school to home in 10 minutes by running, whereas Rahul covers the same distance in 20 minutes by walking. If they start at the same time from school, who shall reach home first?
Sol: We know that the distance covered by objects in a given interval of time can help us to find out which object moves faster than the other.
Manish covers the distance between school and home in 10 minutes and Rahul travels the same distance in 20 minutes. Suppose, Manish and Rahul, leave school at 1 PM. Manish reaches home at 1:10 PM and Rahul reaches home at 1:20 PM. So, Manish reaches home before Rahul.
We can also conclude that Manish moves faster than Rahul.
Tip: Remember the object that moves faster covers a given distance in less time.
(i) Uniform Motion
An object moving along a straight line with a constant or uniform speed is said to be in uniform motion.
Example: The school bus is traveling at a constant speed of 15 km/hr in a straight line, as shown below. Its speed does not change at different points.
(ii) NonUniform Motion
If the speed of an object moving along a straight line keeps changing, then the object is in nonuniform motion.
Example: The speed of the school bus is changing while it moving in a straight line.
Generally, vehicles moving on the road are in nonuniform motion, as they travel at different speeds at different time intervals.
If we have to compare the speeds of a number of objects, then we must express the speeds of all those objects in the same unit.
Conversion of km/hr into m/s and vice versa
Example: A car moves with a speed of 40km/h for 15 minutes and then with a speed of 60km/h for the next 15 minutes. Find the total distance covered by the car.
Sol:
Case 1:
Speed = 40 km/h
Time = 15 min = (15/60) h
Distance (d_{1}) = Speed x Time = 40 x (15/60) = 10 km
Case 2:
Speed = 60 km/h
Time = 15 min = (15/60) h
Distance (d_{2}) = Speed x Time = 60 x (15/60) = 15 km
Total distance (d) = ( d_{1} + d_{2 }) = 10 km + 15 km = 25 km
We measure speed with the help of two main devices  a speedometer and an odometer.
(i) SpeedometerA speedometer is a device on the dashboard of a vehicle that measures and displays the speed of a vehicle. It measures the speed in kilometers per hour.
(ii) OdometerThe distance moved by a vehicle is measured by a device called an odometer. The odometer records the distance traveled by the vehicle in kilometers (km).
Example: The odometer of a car reads 57,321.0 km when the clock shows the time 8:30 AM. The odometer reading was changed to 57,336.0 km. Calculate the speed of the car in km/min during this time. Express the speed in km/h also.
Sol: Initial reading of the odometer of the car at km
Final reading of the odometer of the car km
The car starts at 8:30 AM and stops at 8:50 AM
Distance covered by car = km  km = 15 km
Time taken between 8:30 AM to 8:50 Am = 20 minutes = (20/60) hour =1/3 hour
The SI unit to measure the time is a second. 
Unit of Time:
Type of Clock  Mode to measure time  Image 
Sundial  It uses the position of the sun to depict time  
Sand Clock  It uses sand to measure time  
Water Clock  It uses water to measure time  
Pendulum  It uses a pendulum to measure time  
Quartz Clock  They have an electric circuit that works with the help of cells. They provide accurate time. 
[Question: 982787]
A simple pendulum contains a Bob. It is a metallic ball or a stone that is suspended from a rigid stand with the help of a thread.
Periodic Motion of a Simple Pendulum
Oscillatory motion  The bob of the pendulum does move from the centre (mean position) of the pendulum to its extreme position on the other side. The toandfro motion of the pendulum is called an Oscillatory Motion or a periodic motion.
Oscillation  When the bob moves from its centre (mean position) to its extreme ends it is said to complete one oscillation.
Time Period of a pendulum  The bob starts at its resting point (mean position) and swings to one side (A), then to the other side (B), and back to the middle (O). That whole motion from A to B and back to A is one oscillation. The time taken by the pendulum bob to complete one oscillation is called its Time Period.
The time period of a simple pendulum is given by:
Example: Calculate the time period of a simple pendulum that takes 55 seconds to complete 50 oscillations.
Sol:
Different distancetime graphsThe graphs shown below are distancetime graphs for various types of body motion.
(i) When a body is steady or stationary,
(ii) When a body is moving at a uniform speed,
(iii) When a body is moving nonuniformly with increasing speed, and
(iv) When a body is moving nonuniformly with decreasing speed.
Distancetime graphHere are key observations derived from distancetime graphs:
Making Distance Time Graph
The steps for creating the distancetime graph are given below:
To find the speed of the distancetime graph
Speed = distance/time
= (final position of object – initial position of object)/time taken by object
Also, the speed of the distancetime graph can be calculated by the Slope of a graph. The steeper the slope of the graph, the more is the speed of the object. For example, in the graph given below object A has a steeper slope. This means that object A is moving at a higher speed than object B.
2 straight lines with different slopes
Example: The graph below describes the journey of a man. Determine the speed of the man for each part of the journey.
Sol: We know that ,
From the given graph, we can conclude that,
Example: Jay is going for a drive in his car. The distancetime graph given below describes his full journey. Calculate his total distance traveled during his journey, as well as his average speed between 4:30 and 5:30.
Sol: Jay traveled 30 km away from his home and then stopped for a while. He again drove 20 km and stopped briefly. He then traveled 50 km back home.
So, the total distance traveled by Jay = 30 km + 20 km + 50 km = 100km.
From the axis, we can observe that two big squares total 30 minutes. Hence, one big square is worth 15 minutes. From 4:30 to 4:45, Jay is at rest.
So, his speed between 4:30 and 4:45 = 0/0.25 = 0 km/h.
To calculate the average speed of Jay between 4:30 and 5:30, we need to calculate the slope of the graph between 4:45 and 5:00. This period lasted for 15 minutes, which is equivalent to 0.25 hours – this is the “change in x”.
During this period, he increased his distance from home from 30 km up to 50 km. That means he traveled 20 km in total – this is the “change in y”.
So, we get, slope = 20/0.25 = 80 km/h.
Hence, the average speed = (0 + 80)/2 = 40 km/h
136 videos317 docs54 tests

1. What is the difference between slow and fast speed? 
2. What are the different types of motion? 
3. How is time measured? 
4. What is a distancetime graph? 
5. How can I interpret a distancetime graph? 
136 videos317 docs54 tests


Explore Courses for Class 7 exam
