Negative solutions to positive values

Question

Wondering what negative solutions to equations represent in real life. For example, I was solving a problem that asked for the time when the velocity of a particle is $75\frac{m}{s}$, and I got roughly $6$ and $-11$. What does the $-11$ solution 'mean'. (I don't really know how else to phrase it). The particle is at $75\frac{m}{s}$ at $6s$ and $-11s$?

Answer 1

Sometimes when doing Physics problems, you solve an equation and it gives you more than one answer. It may be mathematically correct, but you need to decide if any of the results makes sense and discard the ones that are impossible to happen in "real life".

Answer 2

The value of $t$ represents a time after a moment in seconds. If $t=6$, then that means $6$ seconds after that specific moment when $t=0$, the velocity is $75~ m \cdot s^{-1}$. If $t=-11$, that implies that the velocity of $75 ~ m\cdot s^{-1}$ was reached $11$ seconds before that specific moment. It is possible that $t$ can be negative. However depending on the context of the question, it is up to you to interpret whether a negative value of $t$ is accepted.

Let's give an example. Let $t$ denote the time in seconds after $11:00~$am. Then you might solve an equation and get $t=120$ and $t=-300$. Then the times are respectively $11:02~$ am and $10:55~$ am.