Derivation of 1st Equation of Motion (Graphical Method)

 Derivation of 1st Equation of Motion (Graphical Method)


Q.:

Derive first equation of motion?

Ans.

Consider a body moving with initial velocity vi in a straight line with uniform acceleration a. Its velocity becomes vf after time t. The motion of body is described by speed-time graph as shown in the figure below

Slope of line AB gives the acceleration ‘a’ of a body.

\[slope of line\overline{AB}=a=\frac{\overline{BC}}{\overline{AC}}=\frac{\overline{BD}-\overline{CD}}{OD}\]

As

\[\overline{BD}=v_{f}\]

\[\overline{CD}=v_{i}\]

\[\overline{OD}=t\]

Putting these values in the above equation we get

\[a=\frac{v_{f}-v_{i}}{t}\]

\[v_{f}-v_{i}=at\]

\[v_{f}=v_{i}+at\]

This is the 1st equation of motion.




 

 

 

 

Comments

Post a Comment

Popular posts from this blog

List of Physics Practicals & Model Paper for Physics Practical of HSSC

Image
  PHYSICS PRACTICALS FOR HSSC   Physics Practical Examinations of students of Federal Board of Intermediate and Secondary Education (FBISE), Islamabad are held after the completion of theory Examination of Higher Secondary School Certificate Part-II (HSSC-II). This is the combined exam for the Practicals of HSSC-I and HSSC-II. LIST OF PRACTICALS   1. Measure length and diameter of a solid cylinder and hence estimate its volume     quoting proper number of significant figures using Vernier callipers. 2. Measure the diameters of a few ball bearings of different sizes using Screw Gauge     and estimate their volumes. Mention the uncertainty in each result. 3. Determine the weight of a body by vector addition of forces. 4. Verify the two conditions of equilibrium using a suspended meter rod. 5. Determine the moment of inertia of a fly wheel. 6. Verify that the time period of the simple pendulum is directly proportional to the     square root of its length and hence find the value of
Read more

List of Physics Practicals & Model Paper for Physics Practical of SSC

Image
PHYSICS PRACTICALS FOR SSC   Physics Practical Examinations of students of Federal Board of Intermediate and Secondary Education (FBISE), Islamabad are held after the completion of theory Examination of Secondary School Certificate Part-II (SSC-II). This is the combined exam for the Practicals of SSC-I and SSC-II. This exam has two sections namely Section-A and Section-B. Section A This section contains Practicals (experiments) related to the theory topics that students studied in Secondary School Certificate Part-I (SSC-I) or (9 th class). Section B This section contains Practicals (Experiments) related to the theory topics that students studied in Secondary School Certificate Part-II (SSC-II) or (10 th class). LIST OF PRACTICALS Section A 1. To measure the volume of a solid cylinder by measuring length and diameter of a solid cylinder     with Vernier calipers. 2. To measure the thickness of a metal strip or a wire by using a screw gauge. 3. To find the accele
Read more

9th Class Physics Chapter 2 (Numerical Problems with Solutions)

Image
  UNIT No. 2 Kinematics (Numerical Problems) 2.1     A train moves with a uniform velocity of 36 kmh -1 for 10 s. Find the distance travelled by it.                                                                                                           Solution                                                                                                                      Data velocity of train = v = 36 kmh -1 = 36 km/h = 36x1000/3600 m/s = 10 m/s                                                                                  Time = t = 10 s Distance travelled by the train = S = ? Formula S = vt Solution S=vt Putting values in this equation S = (10 m/s) (10 s)            S = 100 m          Ans                                 2.2        A train starts from rest. It moves through 1 km in 100 s with uniform  acceleration. What will be its speed at the end of 100 s.?           Solution           Data Initial speed of the train = v i = 0             
Read more