What Are the Units of Constants A and B in the Equation x=At+Bt²?

[tavo0116]

The position of an object is given by x=At+Bt^2, where x is in meters and t is in seconds.
a)What are the units of A?
(express answers in terms of m and s)
b)What are the units of B?
(express answers in terms of m and s)

I know this may sound silly, but I really don't understand what the questions are asking.
Please help, thank you.

 

[ehild]

The dimension of x is length, its unit is meter. The dimension of both At and Bt^2 has to be length. You can multiply and divide dimensions, but you can add quantities of identical dimension only.
So the dimension of At [At]=dimension of A [A] times dimension of time [T], and it has to be length [L]: [At]=[A][T]=[L]. What is the dimension of A then?
If you measure length in meters and time in seconds, what is the unit of A? ehild

 

[tavo0116]

The dimension of x is length, its unit is meter. The dimension of both At and Bt^2 has to be length. You can multiply and divide dimensions, but you can add quantities of identical dimension only.
So the dimension of At [At]=dimension of A [A] times dimension of time [T], and it has to be length [L]: [At]=[A][T]=[L]. What is the dimension of A then?
If you measure length in meters and time in seconds, what is the unit of A?


ehild

Isn't it meters?

 

[ehild]

No. When multiplied by second, it will be meters.

ehild

 

[rwisz]

No problem, I'll break it down for you. The position of an object is a measurement of its location in space. In this equation, x represents the position of the object at a given time, t. A and B are constants that determine how the position changes over time. Now, let's answer the questions:

a) The units of A would be meters per second (m/s). This is because A is multiplied by t, which is in seconds, and the resulting unit would be meters (m). So, A must have the unit of meters per second to cancel out the seconds in t.

b) The units of B would be meters per second squared (m/s^2). This is because B is multiplied by t^2, which is in seconds squared, and the resulting unit would be meters (m). So, B must have the unit of meters per second squared to cancel out the seconds squared in t^2.

I hope this helps clarify the questions for you. Let me know if you have any further questions. As a scientist, it's important to pay attention to units and make sure they are consistent in equations to ensure accurate measurements and calculations.