If s=at^2+bt+c where is distance and is time, what will be the correct unit of a, b, and c
a m/s^2
b m/s
c m
If an object is acted upon only by acceleration a then
x = Xi + Vi t + (1/2) a t^2
Xi is initial position in meters
Vi is initial velocity in x direction in meters/second
a is acceleration in x direction in meters/second^2
if s= at^2 + bt + c where s is distance and t is time. what is the correct unit of a,b and c
The unit of the coefficient 'a' in the equation s = at^2 + bt + c depends on the unit of distance (s) and the unit of time (t). Since s represents distance, it could be in units such as meters, feet, kilometers, or miles. The unit of time (t) is typically measured in seconds, minutes, hours, or any other unit of time.
Given that 's' represents distance, the unit of 'a' would be (unit of distance) per (unit of time^2). For example, if 's' is measured in meters and 't' is measured in seconds, the unit of 'a' would be meters/second^2.
The unit of 'b' also depends on the unit of distance. It would be (unit of distance) per (unit of time), similar to the unit of velocity or speed. For example, if 's' is measured in kilometers and 't' is measured in hours, the unit of 'b' would be kilometers/hour.
Lastly, the constant term 'c' represents a specific value and may not have a specific unit. Its unit will depend on the unit of distance (s).
Therefore, the correct unit of 'a' is (unit of distance) per (unit of time^2), the unit of 'b' is (unit of distance) per (unit of time), and the unit of 'c' will depend on the unit of distance (s).
In the equation s = at^2 + bt + c, the unit of s is distance (such as meters or miles), and the unit of t is time (such as seconds or hours). To determine the correct unit of the coefficients a, b, and c, we need to consider the dimensions on both sides of the equation.
In the equation, the term at^2 represents the acceleration of the object multiplied by the square of time. Acceleration has the unit of distance per time squared (for example, meters per second squared or miles per hour squared). Therefore, the unit of a in the equation is distance per time squared.
The term bt represents the velocity of the object multiplied by time. Velocity has the unit of distance per time (such as meters per second or miles per hour). Therefore, the unit of b in the equation is distance per time.
Finally, the term c is a constant, not dependent on time or distance. Thus, the unit of c in the equation is simply the unit of distance.
To summarize:
- The unit of a is distance per time squared.
- The unit of b is distance per time.
- The unit of c is distance.