If s=at^2+bt+c, where s is distance and t is time, what will be the correct unit of a,b,c
m/s^2, m/s, m
To determine the correct unit for each term in the equation s = at^2 + bt + c, we can look at the units of distance (s) and time (t) and apply dimensional analysis.
The unit of distance (s) is typically expressed in meters (m) or any other unit of length (e.g., miles, kilometers, etc.).
The unit of time (t) is typically expressed in seconds (s), although other units such as minutes or hours can be used depending on the context.
When we look at the equation s = at^2 + bt + c, we can break it down term by term:
1. The term at^2 represents the acceleration (a) multiplied by time squared (t^2). Acceleration has the unit of distance per time squared (e.g., m/s^2).
2. The term bt represents the velocity (b) multiplied by time (t). Velocity has the unit of distance per time (e.g., m/s).
3. The term c represents a constant value, which can be any numerical value without explicitly having units. Therefore, c does not have a specific unit.
In summary, the correct units for each term are:
- The unit for a is distance per time squared (e.g., m/s^2).
- The unit for b is distance per time (e.g., m/s).
- The constant term c is dimensionless (unitless).