Question

Graphically prove that 2as=vf^2_Vi^2​

Answer 1

Answer:

THIRD EQUATION OF MOTION

OR

2aS = Vf2 – Vi2

Initial velocity, final velocity, acceleration, and distance are related in third equation of motion.

Consider a body moving initially with velocity ‘Vi’. After certain interval of time its velocity becomes ‘Vf’. Due to change in velocity, acceleration ‘a’ is produced in the body. Let the body travels a distance of ‘s’ meters.

According to first equation of motion:

Vf = Vi + at

=>Vf – Vi = at

=>(Vf – Vi)/a = t....................(i)

Average velocity of body is given by:

Vav = (Initial velocity + Final velocity)/2

Vav = (Vi + Vf)/2.................. (ii)

we know that :

S = Vav x t.................. (ii)

Putting the value of Vav and t from equation (i) and (ii) in equation (iii)

S = { (Vf + Vi)/2} { (Vf – Vi)/a}

2aS = (Vf + Vi)(Vf – Vi)

According to [ (a+b)(a-b)=a²-b²]

2aS = Vf² –Vi²

Hope this answer helps you out .

Answer 2

Answer:

THIRD EQUATION OF MOTION

OR

2aS = Vf2 – Vi2

Initial velocity, final velocity, acceleration, and distance are related in third equation of motion.

Consider a body moving initially with velocity ‘Vi’. After certain interval of time its velocity becomes ‘Vf’. Due to change in velocity, acceleration ‘a’ is produced in the body. Let the body travels a distance of ‘s’ meters.

According to first equation of motion:

Vf = Vi + at

=>Vf – Vi = at

=>(Vf – Vi)/a = t....................(i)

Average velocity of body is given by:

Vav = (Initial velocity + Final velocity)/2

Vav = (Vi + Vf)/2.................. (ii)

we know that :

S = Vav x t.................. (ii)

Putting the value of Vav and t from equation (i) and (ii) in equation (iii)

S = { (Vf + Vi)/2} { (Vf – Vi)/a}

2aS = (Vf + Vi)(Vf – Vi)

According to [ (a+b)(a-b)=a²-b²]

2aS = Vf² –Vi²

Hope this answer helps you out .

Explanation: