If the change in position Dx is related to velocity v (with units of m/s) in the equation Dx = Av, the constant A has which dimension?
a. m/s^2
b. m
c. s
d. m^2
I chose b?
No.
meters=A*meters/sec
so A has to be seconds.
So it'd be C?
To determine the dimension of the constant A in the equation Dx = Av, we need to analyze the units on both sides of the equation.
The unit of velocity, v, is given as m/s (meters per second).
The unit of the change in position, Dx, is not specified in the given equation.
From the equation Dx = Av, we can deduce that the unit of Dx should be the product of the unit of A and the unit of v.
Options (a) and (d) can be immediately eliminated since they involve square or second power of the unit, which is not supported by the given equation.
Option (c), s (seconds), also does not give a consistent dimension with the equation, as multiplying velocity by seconds does not yield the unit of change in position.
The only remaining option is (b), m (meters). If we multiply the velocity unit m/s with the unit of A, which is meter, we will obtain the unit of change in position, confirming that A has a dimension of meters.
Therefore, you were correct in choosing option (b), m.