Question

Derive third kinematical equation with explanation.

Answer 1

What are the kinematic formulas?

The kinematic formulas are a set of formulas that relate the five kinematic variables listed below.

\Delta x\quad\text{Displacement}ΔxDisplacementdelta, x, start text, D, i, s, p, l, a, c, e, m, e, n, t, end text

t\qquad\text{Time interval}~tTime interval t, start text, T, i, m, e, space, i, n, t, e, r, v, a, l, end text, space

v_0 ~~\quad\text{Initial velocity}~v

0

Initial velocity v, start subscript, 0, end subscript, space, space, start text, I, n, i, t, i, a, l, space, v, e, l, o, c, i, t, y, end text, space

v\quad ~~~\text{Final velocity}~v Final velocity v, space, space, space, start text, F, i, n, a, l, space, v, e, l, o, c, i, t, y, end text, space

a \quad~~ \text{ Constant acceleration}~a Constant acceleration a, space, space, start text, space, C, o, n, s, t, a, n, t, space, a, c, c, e, l, e, r, a, t, i, o, n, end text, space

Why is the time interval now written as t?

If we know three of these five kinematic variables—\Delta x, t, v_0, v, aΔx,t,v

0

,v,adelta, x, comma, t, comma, v, start subscript, 0, end subscript, comma, v, comma, a—for an object under constant acceleration, we can use a kinematic formula, see below, to solve for one of the unknown variables.

The kinematic formulas are often written as the following four equations. Where did these formulas come from?

\Large 1. \quad v=v_0+at1.v=v

0

+at1, point, v, equals, v, start subscript, 0, end subscript, plus, a, t

\Large 2. \quad {\Delta x}=(\dfrac{v+v_0}{2})t2.Δx=(

2

v+v

0

)t2, point, delta, x, equals, left parenthesis, start fraction, v, plus, v, start subscript, 0, end subscript, divided by, 2, end fraction, right parenthesis, t

\Large 3. \quad \Delta x=v_0 t+\dfrac{1}{2}at^23.Δx=v

0

t+

2

1

at

2

3, point, delta, x, equals, v, start subscript, 0, end subscript, t, plus, start fraction, 1, divided by, 2, end fraction, a, t, squared

\Large 4. \quad v^2=v_0^2+2a\Delta x4.v

2

=v

0

2

+2aΔx

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Answer 2

Answer:

The third kinematic formula can be derived by plugging in the first kinematic formula, v = v 0 + a t v=v_0+at v=v0+atv, equals, v, start subscript, 0, end subscript, plus, a, t, into the second kinematic formula, Δ x t = v + v 0 2 \dfrac{\Delta x}{t}=\dfrac{v+v_0}{2} tΔx=2v+v0​​start fraction, delta, x, divided by, t,

Hope it helps

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