Question

If x=a+bt+ct^2,where x is in metres and t in secs. What are units of b and c ?

Answer 1

Answer:

$\purple{\star}$ Unit of b = $\sf{ms^{-1}}$

$\purple{\star}$ Unit of c = $\sf{ms^{-2}}$

Explanation:

Given,

$\sf{x=a + b\;t+c\;t^2}$

Where x is in metres and t is in seconds.

we need to find,

Units of b and c

So,

Since, unit of x is metres therefore,

Dimensionally

$\sf{x=[ L]}$ and $\sf{t=[T]}$

So, Using principle of homogeneity for dimensional equations

$\to \sf{ x = a = [L] }$

$\to\boxed{ \sf{ a = [L]}}\;\; \purple{\star}$

also,

$\to \sf{ x = b \; t = [L]}$

$\to\sf{b\;t=[L]}$

$\to \sf{ b\;.\; [ T] = [L]}$

$\to \sf{ b = \dfrac{[L]}{[T]}}$

$\to \boxed{\sf{b=[LT^{-1}]}}\;\;\purple{\star}$

And,

$\to \sf{ x = c\;t^2 = [L]}$

$\to\sf{c\;t^2=[L]}$

$\\ \to\sf{c\;.\;[T^2]=[L]}$

$\to\sf{c=\dfrac{[L]}{[T^2]}}$

$\to\boxed{\sf{c=[LT^{-2}]}}\;\;\purple{\star}$

Therefore,

Unit of b would be $\sf{ms^{-1}}$, and unit of c would be $\sf{ms^{-2}}$.

Answer 2

Answer:

Question

If x=a+bt+ct^2,where x is in metres and t in secs. What are units of b and c ?

Answer

Unit of b = −1

Unit of c = −2

Explanation

$x \: is \: in \: metre \: \\ t \: is \: in \: second$

We have to find unit of b and c

Dimensiollay

$x \: = (l) \: t \: = (t)$

principle of homogeneity for dimensional equations

➡️ x = a = l

➡️a = [l]

Also,,,,

x = b t = [l]

b t = [ L ]

b. T = [L]

$b \: = \frac{l}{t}$

$\huge \fbox {b = LT-¹}$

And,

➡️x=ct 2 =[L]

➡️ ct ² = L

➡️c. T² =L

$c \: = \frac{ {l} }{ {t}^{2} }$

$\huge \fbox {So the unit will be -1 and -2}$