Question

If v=at+b/t^2+c , find the dimension of a,b and c

Answer 1

Answer:

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Answer 2

Given that,

$v=at+\dfrac{b}{t^2}+c$

Where, v = velocity

t = time

We need to find the dimension of a,b and c

We need to find the dimension of a

Using formula of velocity

$v=at$

$a=\dfrac{v}{t}$

Put the dimension formula

$a=\dfrac{LT^{-1}}{T}$

$a=LT^{-2}$

We need to find the dimension of b

Using formula of velocity

$v=\dfrac{b}{t^2}$

$b =vt^2$

Put the dimension formula

$b=LT^{-1}\times T^{2}$

$b=LT$

We need to find the dimension of c

Using formula of velocity

$v=c$

Put the dimension formula

$c=LT^{-1}$

Hence, The dimension of a, b and c are $LT^{-2}$, LT and $LT^{-1}$