Question

If x=a+bt2, where x is in meter and t in seconds, find the units of 'a'' and 'b'?​

Answer 1

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Question :

Q1) If x=a+bt² , where x is in meter and t is second find the units of a and b?

Given equation :

•x=a+bt²

To find :

•The units of a and b =?

Solution :

$\: \large \red \bigstar \: \bf \: x = a + b {t}^{2}$

Dimensions :

$\\ \large\pink\star \bf { x(distance) = L }$

$\\ \large\green\star\bf{ t(seconds)=T}$

$\\ \implies \large\sf { x=a+bt^2}$

$\\ \implies\large\sf{ L =a +bT^2}$

$\\ \bigstar\underline{\bf{ comparing \: both \: sides}}$

$\\ \implies\underline{ \sf{ a=L }}$

$\\ \therefore\underline{\boxed{\sf{ a=L}}}$

$\\ \implies\large\sf{ L=bT^2}$

$\\ \implies\large\sf{ b=\dfrac{L}{T^2}}$

$\\ \implies\large\sf{ b= LT^{-2}}$

$\\ \therefore\underline{\boxed{\sf{b=LT^{-2}}}}$

$\\ \large\blue\bigstar\boxed{\underline{\bf { a=metre \: and \: b=metre/(second)²=ms^{-2} . \: ie (velocity)}}}$