Equation z = ct + d, z is measured in meters and t in seconds; dimensions of D?

AI Thread Summary
In the equation z = ct + d, where z is in meters and t is in seconds, the dimensions of d must match those of z to maintain unit consistency. Therefore, d must also be measured in meters. The discussion emphasizes that adding terms with different units, such as meters and amperes, is not valid in physical equations. The conclusion is that d must equal meters for the equation to be dimensionally consistent. This ensures that all terms in the equation have the same units.
William2
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Homework Statement


In the equation z = ct + d, z is measured in meters and t is measured in seconds. What are the dimensions (units) of d?

answer options are...
s/m, m/s, m, s, m*s

Homework Equations


The Attempt at a Solution



plugged in m for z, s for t, and m/s for c. solved for D and got 0.
 
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Assume that z is not equal to ct, then if you solve for d, what do you get?
 
rcgldr said:
Assume that z is not equal to ct, then if you solve for d, what do you get?

ermm...i'm guessing m?
 
Would it make sense to add two terms together that had different units? Like adding 5 meters plus 35 Amperes?
 
Can you solve for d and show the equation?

d = ?
 
All the individual terms in a physical equation have to have the same units.
 
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