If s =at^2+bt+c. What is the correct units of a,b and c?
if s is meters, then
a is meters/sec^2
b is meters/sec
c is meters
a ... m/s^2 ... acceleration
b ... m/s ... velocity
c ... m ... distance
To determine the correct units of the variables a, b, and c in the equation s = at^2 + bt + c, we need to consider the dimensions of each term in the equation as well as the final dimension of the equation.
In this equation, s represents displacement or length, and t represents time. Since time squared (t^2) appears in the equation, we know that the dimensions of a must correspondingly be length divided by time squared (L/T^2).
Now, let's examine the right-hand side of the equation. We have three terms: at^2, bt, and c.
The second term, bt, can be deduced to have the same dimensions as s. Therefore, the dimensions of b must be length divided by time (L/T).
Finally, we have the constant term c, which represents a value with no physical dimensions. So, the dimensions of c are simply numerical or dimensionless.
To summarize:
- The dimensions of a are L/T^2 (length divided by time squared).
- The dimensions of b are L/T (length divided by time).
- The constant term c is dimensionless.
By understanding the physical meaning and dimensions of each term, we can determine the correct units of a, b, and c in the equation s = at^2 + bt + c.