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

S = u t  + 1/2 a t*t 

a t = [ a ] [ T ] = dimension of x = meters
so a = meters / sec 

[ a ] [ T ² ] =  dimension of x  = meters

so a = meters/ sec²

Answer 2

Answer:

The unit of a is m/s and unit of b is $\bold{m / S^{2}}$

Explanation:

Here the formula given is, $\bold{x=a t+b t^{2}}$

And it is clearly mentioned that x is in meters and t is in seconds. So units of a and b must be containing meter and second.

Now Let’s start with x = at So a = x/t --------(1)

$x=b t^{2}$ so $\mathrm{b}=\mathrm{x} / \mathrm{t}^{2}$ ------(2)

Now as per the dimension formula, we can find unit of a and b.

As per equation (1), a = unit of x/ unit of t  

                                  = Length / Time = L / T ---(3)

As per equation (2), b = unit of x / unit of  $t^{2}$

$=\text { Length } / \text { Time }^{2}=\mathrm{L} / \mathrm{I}^{2}$ T2  -----(4)

So Unit of a according to equation (3) = m / S

And Unit of b according to equation (4)  =  $m / S^{2}$