Physics, asked by deepak4250pubg, 1 year ago

write and derive the equation of motion involving uniform acceleration

Answers

Answered by sukhman256

Explanation:

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Answered by aanyasharmac20

Answer:

1. Deriving the Equation for Velocity – Time Relation:

Acceleration = Change in velocity / time taken

Acceleration = (final velocity – initial velocity) / time

a = (v – u)/t

so, at = v – u

v = u + at

2. Deriving Equation for Position – Time Relation:

We know that, distance travelled by an object = Area under the graph

So, Distance travelled = Area of OPNR = Area of rectangle OPQR + Area of triangle PQN

s = (OP * OR) + (PQ * QN) / 2

s = (u * t) + (t * (v – u) / 2)

s = ut + 1/2 at2 [because at = v – u]

3. Deriving the Equation for Position – Velocity Relation

We know that, distance travelled by an object = area under the graph

So, s = Area of OPNR = (Sum of parallel sides * height) / 2

s = ((PO + NR)* PQ)/ 2 = ( (v+u) * t)/ 2

2s / (v+u) = t [equation 1]

Also, we know that, (v – u)/ a = t [equation 2]

On equating equations 1 and 2, we get,

2s / (v + u) = (v – u)/ a

2as = (v + u) (v – u)

2 a s = v2 – u2

Hope this helps!

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