**v ^{2}- u**

^{2 }=

**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 = V^{2} - U^{2} / 2A

2AS = V^{2} - U^{2}

OR V^{2 - }U^{2 }= As

Hence,Derived..!

- 56

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