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/s2
b) m
c) s
d) m2
I'm not sure how to eliminate the seconds from the velocity. Thanks in advance for any help!
velocity * time = change in location (Dx)
Therefore the answer is c) seconds
Quantities must have different units before they can be added or subtracted.
To determine the dimension of the constant A in the equation Dx = Av, we need to consider the dimensions of both Dx and v.
The dimension of Dx is given as meters (m). The dimension of v is given as meters per second (m/s).
By comparing the two terms, we can see that the velocity v has "seconds" in the denominator. To eliminate the seconds, we need to multiply v by a constant that has the dimension of seconds. This is because when meters per second is multiplied by seconds, the seconds cancel out, leaving only meters.
Therefore, the constant A must have the dimension of seconds (s). So, the correct answer is c) s.
To determine the dimension of the constant A in the equation Dx = Av, we can analyze the units involved.
The units of Dx are meters (m) as it represents a change in position. The units of velocity v are meters per second (m/s) since it represents the rate at which the position changes over time.
To determine the units of A, we need to eliminate the seconds from the velocity units. We can achieve this by dividing the velocity v by time, which gives us the acceleration. The unit of acceleration is meters per second squared (m/s^2).
Therefore, the constant A in the equation Dx = Av must have the same units as the change in position Dx, which is meters (m). Consequently, the correct answer is (b) m.