In the relation a = bt + X, a and X are measured in metre (m) and t is measured in second (s). The SI unit of b must be

According to the principle of dimensional homogeneity, all terms in a physical equation must have the same dimensions and units [t2][t3]. In the given relation a = bt + X, the variables 'a' and 'X' are measured in metres (m). Therefore, the term 'bt' must also have the unit of metres to be added to 'X' and equate to 'a' [t2]. Since 't' is measured in seconds (s) [c2][c4], the unit of 'b' multiplied by seconds must equal metres (b × s = m). Solving for 'b' gives the unit as metres per second (m/s), which is expressed as ms^-1 [c1][t2]. This follows the standard analysis where constants in position-time equations represent physical quantities like velocity or acceleration depending on their power of 't' [t1][t3]. Thus, the SI unit of b is ms^-1.

Sources

1. [1] Science-Class VII . NCERT(Revised ed 2025) > Chapter 8: Measurement of Time and Motion > 8.1.2 SI unit of time > p. 111
2. [2] Science-Class VII . NCERT(Revised ed 2025) > Chapter 8: Measurement of Time and Motion > In a Nutshell > p. 118
3. [3] Science-Class VII . NCERT(Revised ed 2025) > Chapter 8: Measurement of Time and Motion > Speed = Total distance covered Total time taken > p. 113