Question

prove that
$s = ut + \frac{1}{2} a {t}^{2}$
​

Answer 1

here is your answer :

LHS

= [ s ]

= [ L ]

Again,

RHS,

= [ ut+ 1/2 at^2]

= [ut]+ [at^2] •.• 1/2 has no dimension

= [LT^-1•T] + [LT^-2•T^2]

= [L]+ [L]

= [L] •.• 2 has no dimension

hence proved

Answer 2

Answer.

Consider an object moving with initial velocity u and acceleration a for time t so that its final velocity becomes v. Let the distance travelled by the body be s.

Average Velocity =

$\frac{total \: distance \: travelled}{total \: time \: taken}$

$= \frac{s}{t} \: \: ...(1)$

Also, average velocity

$\frac{u + v}{2} \: \: ...(2)$

From (1) and (2),

$\frac{s}{t} = \frac{u + v}{2}$

From first equation of motion,

$v = u + at \: \: ...(3)$

Substituting the value of v from (3) in (2),

$\frac{s}{t} = \frac{u + u + at}{2}$

$⇒ \: s = \frac{(2u + at)t}{2}$

$⇒ \: s = \frac{2ut + a {t}^{2} }{2}$

$⇒ \: s = ut \: + \frac{1}{2}a {t}^{2}$

Hence, proved.

Please mark the BRAINLIEST.

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