Question

obtain equations of motion for constant acceleration using method of calculus

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Answer 1

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Answer 2

Answer:

we know ,

acceleration is the change in velocity per unit time .

e.g an instant time ; a = dv/dt

a = dv/dt

a∫dt = ∫dv

now, integrate

a.(t₂ - t₁) = v - u

Let (t₂- t₁) = t

then, at = v - u

v = u +mark me as ___ its a motion equation ,

_______________________________

now ,

v = u + at

multiply both sides, with dt

v.dt = u.dt + at.dt

we know, v.dt = S { distance = speed * time } use this

S = u(t₂-t₁) + a(t₂-t₁)²/2

hence,

S = ut + 1/2at² ___motion, equation.

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now,

S = ut + 1/2at² ___(1)

v = u + at

squaring both sides,

v² = u² + a²t² + 2uat

v² = u² + 2a{ 1/2at² + ut }

from eqn (1)

v² = u² + 2aS ____motion equation,

__________________________________

or

we know,

v.dv/dx = a

∫v.dv = a∫dx

integrate both sides,

v² - u² = 2a( x₂ - x₁)

Let ( x₂ - x₁) = S

v² = u² + 2aS___motion equation

____________________________________________________________________________

Explanation:

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