Final answer:
The dimension of b is speed (length over time, L/T), with SI units of meters per second (m/s). The dimension of c is acceleration (length over time squared, L/T^2), and its SI unit is meters per second squared (m/s^2).
Step-by-step explanation:
When analyzing the equation y = a + bt + ct^2, where y represents the distance and t represents the time, the dimensions of both b and c need to be determined to ensure dimensional consistency. In this context, a would have the dimensions of length (L), since it is a constant that adds directly to the distance y.
In order for the equation to be dimensionally consistent, each term must have the same dimensions. The term bt indicates that b must have the dimension of speed, which is length over time (L/T). Therefore, the SI unit of b is meters per second (m/s). As for the term ct^2, c must have the dimension of acceleration, which is length over time squared (L/T^2), since when multiplied by t^2 (time squared), it should result in a length dimension. Consequently, the SI unit for c is meters per second squared (m/s^2).