Question
If $$x = at + b{t^2},$$ where $$x$$ is the distance travelled by the body in kilometer while $$t$$ is the time in second, then the unit of $$b$$ is
A.
$$km/s$$
B.
$$km - s$$
C.
$$km/{s^2}$$
D.
$$km - {s^2}$$
Answer :
$$km/{s^2}$$
Solution :
As $$x = at + b{t^2}$$
According to the concept of dimensional analysis and principle of homogeneity
$$\eqalign{
& \therefore \,{\text{unit}}\,{\text{of}}\,x = {\text{unit}}\,{\text{of}}\,b{t^2} \cr
& \therefore \,{\text{unit}}\,{\text{of}}\,b = \frac{{{\text{unit}}\,{\text{of}}\,x}}{{{\text{unit}}\,{\text{of}}\,{t^2}}} = km/{s^2} \cr} $$