Question

If x = at + bt2 where x is in meters and t is in seconds. What are the units of a and b?
CLASS - XI PHYSICS (Physical World & Measurement)

Answer 1

at,bt2 should have the same dimensions as x.

Answer 2

Answer:

The unit of a and b are m/s and m/s².

Explanation:

Given that,

$x = at+bt^2$....(I)

Here, x = meters

t = seconds

From equation (I)

$x = at$

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

The dimension of x = L

The dimension of  t = T

The dimension formula of a is

$a=\dfrac{[L]}{[T]}$

$a=[LT^{-1}]$

The unit of a is m/s.

Again, from equation (I)

$x= bt^2$

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

The dimension formula of b is

$b=\dfrac{L}{T^2}$

$b=[LT^{-2}]$

The unit of b is $m/s^2$

Hence, The unit of a and b are m/s and m/s².