Question

In the equation of motion y = at + bt ^2, the units of a and b are respectively
(a) m, ms^-2
(b) ms^-1 , ms^-2
(c)m,m
(d) none of these ​

Answer 1

Answer:

According to the principle of homogeneity of dimension, an equation is dimensionally correct when each term has same dimension on both sides of the equation.

Thus, [x]=[at] and [x]=[bt

2

]

So, [a]=[x/t] and [b]=[x/t

2

]

As x has dimension of length and t has dimension of length so unit of a will be m/s and unit of b will be m/s

2

.