Question

equation of motion for a particle having uniform acceleration ​

Answer 1

Answer:

Explanation:

see diagram, a particle starts to move from A with velocity u and a constant acceleration acting on particle is a. after time t, particle reach the point B where velocity of particle is v.

from definition of acceleration, slope of velocity time graph gives acceleration,

so acceleration, a = (v - u)/t

or, at = v - u

⇒[ v = u + at ].....(1)

again, we know, displacement is equal to area under the velocity time graph.

area of AOEB = displacement, s = 1/2 [AO + BE ] × OE

or, s = 1/2 (u + v) × t

or, s = 1/2 (u + u + at) × t [ from eq. (1) ]

or, s = 1/2 (2u + at) × t

⇒[ s = ut + 1/2at² ]......(2)

squaring equation (1),

v² = (u + at)²

= u² + a²t² + 2uat

= u² + 2a(1/2at² + ut)

= u² + 2a(ut + 1/2 at²)

= u² + 2as [ from eq . (2) ]

⇒[v² = u² + 2as ].......(3)

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