X(t) = 5t^2 + 2t + 3
What are the units for 5? 2? 3?
In a physics problem, the "t" represnts time, in any convenient units (usually seconds), and the coefficients (5,2,3 in this case) have diffent dimensions so that the productwith t^n has dimentions of length. The 5 in your equation would have dimensions of acceleration; the 2 would have dimensions of speed and the 3 would have dimensions of length.
so it would be m/(s^3) m/(s^2) and m?
I know acceleration is m/(s^2) not m/(s^3) but the 5 in the equation is 5t^3
So is my first guess right or second?
The first term in your equation is 5 t^2, not 5 t^3. The dimensions of the 5 would be m/s^2 if X is in meters and t is in seconds.
No on my packet it says X(t) = 5t^3 + 2t^2 + 3 so...
That is not what you first posted. It was
<<X(t) = 5t^2 + 2t + 3 >>
If it is 5t^3 + 2t^2 + 3, then you have to change the dimensions of the 5 and 2 to what you said.
To determine the units of the coefficients in the equation X(t) = 5t^2 + 2t + 3, we need to understand what each term represents.
In this equation, X(t) represents the position or value of the function at a given time t. The units of X(t) will depend on the context of the problem or system being modeled.
Now, let's look at the coefficients individually:
1. The coefficient 5: In this equation, the coefficient 5 multiplies the term t^2. Since t^2 represents the square of time, the units for 5 will be determined by the units of X(t) divided by the square of the units of time. For example, if X(t) represents a distance in meters and t represents time in seconds, then the units for 5 would be meters per second squared (m/s^2).
2. The coefficient 2: In this equation, the coefficient 2 multiplies the term t. Since t represents time, the units for 2 will be determined by the units of X(t) divided by the units of time. Using the same example as before, if X(t) represents a distance in meters and t represents time in seconds, then the units for 2 would be meters per second (m/s).
3. The coefficient 3: In this equation, the coefficient 3 is a constant term that does not involve any multiplication with t. Therefore, the units for 3 will be the same as the units of X(t). Continuing with the previous example, if X(t) represents a distance in meters, then the units for 3 would also be meters.
To summarize, the units for 5, 2, and 3 in the given equation depend on the units of X(t) and the units of time used in the problem or system being described.