Question

The velocity of a particle is given as $v=a+bt+c{t}^2$ .the velocity is measured in ${ms}^{-1}$ , then units of a and c are

• A. $m{s}^{-1}\text{and}m{s}^{-3}$
• B. $m{s}^{-2}\text{and}ms$
• C. $m^{2}s\text{and}m{s}^2$
• D. $ms\text{and}m{s}^{-1}$

Answer 1

The correct option is A $m{s}^{-1}\text{and}m{s}^{-3}$

The magnitudes of physical quantities can be added together or subtracted from one another only if they have the same dimensions.

$\left[a\right]=\left[u\right]=m{s}^{-1}$

$\left[c{t}^2\right]=\left[v\right]=m{s}^{-1}$

$\left[c\right]=\left[\frac{v}{s^2}\right]=m{s}^{-1-2}$

$\left[c\right]=m{s}^{-3}$

Option A