Previously we have discussed regarding speed,velocity, acceleration of one dimensional motion.Here we are going to extend that more in detail and going through the above posts will definitely help in understanding the present concepts.
Basic definitions of Kinematics :
It is nothing but one dimensional motion where body always moves along a line.We can derive the following formula in the case of linear motion.
1 . Average velocity V = Total displacement / Total time
Avg.velocity = s1+s2+s3/t1+t2+t3 where t1 is time in the first case where as s1 is the displacement in the first case and so on.
2 . If a body travels with a velocity v1 for the first half of the journey time and with a velocity v2 for the second half of the journey time, then the average velocity is equal to v1+v2/2.
3 . If a body covers first half of its journey with uniform velocity v1 and the second half of the journey with uniform velocity v2, then the average velocity is equal to 2v1v2/v1+v2 .
4 . If a body travels first one third of the distance with a speed v1, and second one third of the distance with a speed v2 and the last one third of the distance with a speed v3 then the average velocity is 3v1v2v3/v1v2+v2v3+v3v1.
5. The rate of change of velocity is called acceleration.
Equations of motion for a body moving with uniform acceleration
The following equations represent the motion of a body under constant acceleration.
If a body starts from rest and having uniform acceleration then the above equations can be modified as shown below.
Please click on the screen for a better view.
Notes :
1 . If the velocity of a body becomes 1/n of original velocity after a displacement x then it will come to rest after covering a further displacement of X/n2 - 1 .
2 . A body is describing uniform circular motion with a speed ‘v’. When it describes an angle ‘q’ at the center then the change in velocity is dv = 2vsin (q/2)
3 . If the displacement of a body is proportional to the square of time, then its initial velocity is zero.
4 . Starting from rest a body travels with an acceleration ‘a’ for some time and then with deceleration ‘b’ and finally comes to rest. If the total time of journey is ‘t’, then the maximum velocity and displacement and average velocity are respectively then
i) Maximum velocity = ab t/a + b
ii) Displacement s = abt2/2(a+b).
iii)Average Velocity = maximum velocity / 2.
5 . If a particle starts from rest and moves with uniform acceleration ‘a’ such that it travels distances X and Y in the m and n particular seconds then
sn/s = X-Y/m-n where n is the particular second of journey.
6 . A particle starts from rest and moves along a straight line with uniform acceleration. If s is the distance traveled by it n seconds and S is the distance travel led in the particular n th second then sn/s = 2n-1 /n2
Basic definitions of Kinematics :
- The study of motion of objects without any reference to the cause of motion is called kinematics.
- The actual path traversed by a body is called the distance traveled.
- The shortest distance between the initial and final positions of a body is called displacement.
- Displacement of a body may be zero, or positive or negative but distance traveled is always positive.
- The speed of a body is the rate at which it describes its path.
- The rate of change of displacement is called velocity.
- Average speed = total distance / total time
- Average velocity = net displacement / total time
It is nothing but one dimensional motion where body always moves along a line.We can derive the following formula in the case of linear motion.
1 . Average velocity V = Total displacement / Total time
Avg.velocity = s1+s2+s3/t1+t2+t3 where t1 is time in the first case where as s1 is the displacement in the first case and so on.
2 . If a body travels with a velocity v1 for the first half of the journey time and with a velocity v2 for the second half of the journey time, then the average velocity is equal to v1+v2/2.
3 . If a body covers first half of its journey with uniform velocity v1 and the second half of the journey with uniform velocity v2, then the average velocity is equal to 2v1v2/v1+v2 .
4 . If a body travels first one third of the distance with a speed v1, and second one third of the distance with a speed v2 and the last one third of the distance with a speed v3 then the average velocity is 3v1v2v3/v1v2+v2v3+v3v1.
5. The rate of change of velocity is called acceleration.
Equations of motion for a body moving with uniform acceleration
The following equations represent the motion of a body under constant acceleration.
If a body starts from rest and having uniform acceleration then the above equations can be modified as shown below.Please click on the screen for a better view.
Notes :
1 . If the velocity of a body becomes 1/n of original velocity after a displacement x then it will come to rest after covering a further displacement of X/n2 - 1 .
2 . A body is describing uniform circular motion with a speed ‘v’. When it describes an angle ‘q’ at the center then the change in velocity is dv = 2vsin (q/2)
3 . If the displacement of a body is proportional to the square of time, then its initial velocity is zero.
4 . Starting from rest a body travels with an acceleration ‘a’ for some time and then with deceleration ‘b’ and finally comes to rest. If the total time of journey is ‘t’, then the maximum velocity and displacement and average velocity are respectively then
i) Maximum velocity = ab t/a + b
ii) Displacement s = abt2/2(a+b).
iii)Average Velocity = maximum velocity / 2.
5 . If a particle starts from rest and moves with uniform acceleration ‘a’ such that it travels distances X and Y in the m and n particular seconds then
sn/s = X-Y/m-n where n is the particular second of journey.
6 . A particle starts from rest and moves along a straight line with uniform acceleration. If s is the distance traveled by it n seconds and S is the distance travel led in the particular n th second then sn/s = 2n-1 /n2
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