Question

If $x=at+b{t}^2$, where $x$ is the distance travelled by the body in kilometer while $t$ is the time in seconds, then find the units of $b$.

Answer 1

$x=at+{bt}^2$

$x$ is in meter. $t$ is in second.

Applying law of homogenity.

$b=\frac{\left[x\right]}{\left[t^2\right]}$

$b=\frac{m}{s^2}\Rightarrow b=m/{sec}^2$