v2- u2 = 2as
since, S (Distance) = Average speed x Time
S = U+V / 2 * T
S = U+V / 2 * V - U / A {since T = V -U / A}
S = V2 - U2 / 2A
2AS = V2 - U2
OR V2 - U2 = As
Hence,Derived..!
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For this equation we need 2 equations as base which are : s = v+u/2 * time and t = v-u/a
s(average velocity)= v + u/2 * time
In the equation we don't want time, so we will use the equation t= v-u/a derived from 1st equation of motion
=> s = v+u/2*v-u/a
=> s = (v+u)(v-u)/ 2*a
=> s = v^2 - u^2 / 2a
=> 2as = v^2 - u^2
=> 2as + u^2 = v^2
Hence proved..
s(average velocity)= v + u/2 * time
In the equation we don't want time, so we will use the equation t= v-u/a derived from 1st equation of motion
=> s = v+u/2*v-u/a
=> s = (v+u)(v-u)/ 2*a
=> s = v^2 - u^2 / 2a
=> 2as = v^2 - u^2
=> 2as + u^2 = v^2
Hence proved..
- 1
Uniform Motions:-
1.The hour hand of a clock - It moves with uniform speed, completing movement of a specific distance in an hour
2.A car going along a straight level road at steady speed
3.An aircraft cruising at a level height and a steady speed
4.A ship steaming on a straight course at steady speed
5.A train going along the tracks at steady speed
6.A cooling fan running at a fixed speed
7.Earth moving round the sun is an uniform motion
8. Movement of fan
9. A pendulum having equal amplitudes on both sides
10. A vibrating spring in a sewing machine
11. Rain drops fall at uniform speed as buoyant forces balances 'g'
Non uniform Motions:-
1. A horse running in a race
2. A bus on its way through the market
3. A bouncing ball
4. Movement of an asteroid
5. Aircraft moving through the clouds and then landing
6. Dragging a box from a path
7. A man running a 100 m race
8. A car coming to a halt
9. A train coming to its terminating sop
10. A car colliding with another car
In the above motions, the speed of varying
- -2
When the speed of an obj is constantly changing,the instantaneous speed is the speed of an obj at a particular moment in time. For ex- A cheetah who is runningwith the speed of 80 mins per hour then it is shown as in per hour speed.
The velocity of an obj in motion at a specific point in time. If an obj has a standard velocity over a period of time its average and instantaneous velocity.
- -1
Since, the third equation of motion is given as hereunder:-
V?-U?=2as where
V=final velocity
U=initial velocity
a=Acceleration
s= Displacement
So the derivation of equation is given hereunder:-
Since, Displacement= average velocity ?Time
So, S= v+u?2 ? v-u?a(acceleration)
S=V?-U??2a
So , V?-U?=2as ( by transvering )
V?-U?=2as where
V=final velocity
U=initial velocity
a=Acceleration
s= Displacement
So the derivation of equation is given hereunder:-
Since, Displacement= average velocity ?Time
So, S= v+u?2 ? v-u?a(acceleration)
S=V?-U??2a
So , V?-U?=2as ( by transvering )
- -1
From the velocity - time graph the distance 's' covered by an object in time(t) moving with uniform accelerated motion is the area enclosed by the trapezium OABC under the graph.
Distance(s) = Area of trapezium OABC
s =1/2 (OA +BC)OC
s =1/2 (u+v)t
s = t = v - u / a
s = 1/2 (v+u) (v-u/a)
2as =(v+u) (v-u)
2 2
2as = v - u
Distance(s) = Area of trapezium OABC
s =1/2 (OA +BC)OC
s =1/2 (u+v)t
s = t = v - u / a
s = 1/2 (v+u) (v-u/a)
2as =(v+u) (v-u)
2 2
2as = v - u
- 0
Uniform Motions:- 1.The hour hand of a clock - It moves with uniform speed, completing movement of a specific distance in an hour 2.A car going along a straight level road at steady speed 3.An aircraft cruising at a level height and a steady speed 4.A ship steaming on a straight course at steady speed 5.A train going along the tracks at steady speed 6.A cooling fan running at a fixed speed 7.Earth moving round the sun is an uniform motion 8. Movement of fan 9. A pendulum having equal amplitudes on both sides 10. A vibrating spring in a sewing machine 11. Rain drops fall at uniform speed as buoyant forces balances 'g' Non uniform Motions:- 1. A horse running in a race 2. A bus on its way through the market 3. A bouncing ball 4. Movement of an asteroid 5. Aircraft moving through the clouds and then landing 6. Dragging a box from a path 7. A man running a 100 m race 8. A car coming to a halt 9. A train coming to its terminating sop 10. A car colliding with another car In the above motions, the speed of varying
- 0