Calculate the SI units of the constants A and B in each of the following equations. Assume that the distance x is in meters (m), the time t is in seconds (s), and the velocity v is in meters per second (m/s).
a. x = A + B.t
Meters = A + B * seconds
b. x = ¼ A.t2
Meters = 0.25 * A * seconds^2
c. v2 = 4.A.x
M/s^2 = 4 * A * meters
To calculate the SI units of the constants A and B in each equation, we need to look at the dimensions on both sides of the equation. The SI units of a physical quantity represent its dimensions and are often written in terms of fundamental units such as meters (m), seconds (s), kilograms (kg), etc.
a. In the equation x = A + B.t:
- The left-hand side of the equation represents a distance in meters (m).
- The first term on the right-hand side represents a constant (A) which should have the same dimensions as the distance (meters).
- The second term on the right-hand side should have the same dimensions as the time (seconds).
So, the SI unit of A is meters (m) and the SI unit of B is 1/seconds (1/s).
b. In the equation x = ¼ A.t^2:
- The left-hand side represents a distance in meters (m).
- The first term on the right-hand side represents a constant (A) which should have the same dimensions as the distance (meters).
- The second term on the right-hand side represents time squared (seconds^2).
So, the SI unit of A is meters (m) and the SI unit of B is 1/seconds^2 (1/s^2).
c. In the equation v^2 = 4.A.x:
- The left-hand side represents velocity squared (meters^2/seconds^2).
- The constant 4 should have the same dimensions as the right-hand side.
- The term A represents a constant that should have the same dimensions as the velocity squared (meters^2/seconds^2).
- The term x represents distance in meters (m).
So, the SI unit of A is meters^2/seconds^2 (m^2/s^2) and there is no constant B in this equation.
Remember, when calculating the SI units of constants in an equation, it is important to pay attention to the dimensions on both sides of the equation and ensure that they match.