Long Term Courses *    67 Selections in IIT JEE 2012 *    192 Selections in AIEEE 2012 *    19 Selections in AIPMT 2012 *    330 Students score 90% + in CBSE-XII Board 2013 *    445 Students score 10 CGPA in CBSE-X Board 2013
Attend Free Demo Class Now
Name
 
Contact Number
 
 
Email ID
 
 
Class
 
City
 
   
 
Contact our Toll Free Nos
  • India Toll Free : 1-800-3070-0017
  • Bahrain (National) : 973-16198627
  • Indonesia Toll Free : 1-803-015-204-5864
  • Singapore (National) : 65-31586005
  • USA/Canada Toll Free : 1-888-442-3128
  • Others : +91-9899713975
 
operations_kei 09718199348 Login Reg
IITians @ your home
ISO 9001:2008 Certified

MOTION

Graphical Representation of Motion


Graphs provide a convenient method to present basic information about a variety of events. For example, in the telecast of a one-day cricket match, vertical bar graphs show the run rate of a team in each over. As you have studied in mathematics, a straight line graph helps in solving a linear equation having two variables. To describe the motion of an object, we can use line graphs. In this case, line graphs show dependence of one physical quantity, such as distance or velocity, on another quantity, such as time.

Distance-Time Graphs

The change in the position of an object with time can be represented on the distance-time graph adopting a convenient scale of choice. In this graph, time is taken along the x–axis and distance is taken along the y-axis. Distance-time graphs can be employed under various conditions where objects move with uniform speed, non-uniform speed, remain at rest etc.

Figure- (Distance-Time Graphs)

We know that when an object travels equal distances in equal intervals of time, it moves with uniform speed. This shows that the distance travelled by the object is directly proportional to time taken. Thus, for uniform speed, a graph of distance travelled against time is a straight line, as shown in Fig. 3. The portion OB of the graph shows that the distance is increasing at a uniform rate. Note that, you can also use the term uniform velocity in place of uniform speed if you take the magnitude of displacement equal to the distance travelled by the object along the y-axis.

We can use the distance-time graph to determine the speed of an object. To do so, consider a small part AB of the distance-time graph shown in Fig 3. Draw a line parallel to the x-axis from point A and another line parallel to the y-axis from point B. These two lines meet each other at point C to form a triangle ABC. Now, on the graph, AC denotes the time interval (t2 – t1) while BC corresponds to the distance (s2 – s1). We can see from the graph that as the object moves from the point A to B, it covers a distance (s2 – s1) in time (t2 – t1). The speed, v of the object, therefore can be represented as

Figure- (Distance-Time Graphs)

We can also plot the distance-time graph for accelerated motion. Table shows the distance travelled by a car in a time interval of two seconds.

The distance-time graph for the motion of the car is shown in Fig. 4. Note that the shape of this graph is different from the earlier distance-time graph (Fig. 3) for uniform motion. The nature of this graph shows nonlinear variation of the distance travelled by the car with time. Thus, the graph shown in Fig 4 represents motion with non-uniform speed.

Figure- (Distance-Time Graphs)
Figure- (Distance-Time Graphs)

Do you like this Topic?

Share it on


       
       
Online Classroom Program Online Classroom Program 1 on 1 Online Classes 1 on 1 Online Classes Correspondence Course Correspondence Course Correspondence Course Best Pool of Faculty Result Oriented Coaching Program

Welcome to Kshitij Education India

Our Guarantee:

We're so sure you'll have the time of your life with us, we back our courses with a 100% Satisfaction Guarantee.

If for any reason you aren't 100% satisfied with your classes in first 7 days, just let us know and we'll refund your fees. No questions asked.

And based on your feedback, we will take the necessary steps to ensure we never repeat any mistakes as such.

Satisfaction Guaranteed
Live Chat