Question

Define redondation - Prove that s=u+1/2a2+1+2
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Answer 1

Correct Question:

• Define retardation.

• Prove that : s = ut + ½at²

Requirer Answer:

Answer 1st:

→ Retardation is the change in velocity with time. In actual way, retardation is the acceleration with the negative sign.

• SI unit of retardation is m/s².

• It is a vector quantity.

• Formula : v-u/t

Where,

v = final velocity

u = initial velocity

t = time.

Answer 2nd:

Let us assume the distance travelled as 's'. The distance travelled by a moving body in time (t) can be found by using average velocity. As the intial velocity of the body is 'u' and its final velocity is 'v', so the average velocity will be

→ $\sf { Velocity_{avg} = \dfrac{Initial \: velocity + Final \: velocity}{2} }$

or,

$\sf { Velocity_{avg} = \dfrac{u + v}{2} }$

Also, we know that:

Distance travelled = Average velocity × time

or we can write it as,

$\sf { s= \dfrac{u + v}{2} \times t}$.............. ( i )

Now, from the first equation of motion we know that,

• v = u + at

So, substitute the value of v in the equation (i) :

$\sf { \longmapsto s= \dfrac{(u + u + at) \times t}{2} }$

$\sf { \longmapsto s= \dfrac{(2u+ at )\times t}{2} }$

$\sf { \longmapsto s= \dfrac{2ut + a{t}^{2} }{2} }$

${\underline {\boxed {\small {\sf \pink { s = ut + \dfrac{1}{2}a{t}^{2} } }}}}$

Hence, proved!

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