To determine how long it will take to stop when running at an initial speed of [tex]\( 6 \, \text{m/s} \)[/tex] and decelerating at a rate of [tex]\( 2 \, \text{m/s}^2 \)[/tex], follow these steps:
1. Identify the Known Values:
- Initial speed ([tex]\( v_i \)[/tex]): [tex]\( 6 \, \text{m/s} \)[/tex]
- Deceleration ([tex]\( a \)[/tex]): [tex]\( 2 \, \text{m/s}^2 \)[/tex]
2. Understand the Relationship Between Speed, Deceleration, and Time:
To find the time ([tex]\( t \)[/tex]) it takes to come to a stop, we can use the formula:
[tex]\[
t = \frac{v_i}{a}
\][/tex]
3. Plug in the Known Values into the Formula:
[tex]\[
t = \frac{6 \, \text{m/s}}{2 \, \text{m/s}^2}
\][/tex]
4. Simplify the Expression:
[tex]\[
t = 3 \, \text{seconds}
\][/tex]
5. Interpret the Result:
It will take [tex]\( 3 \)[/tex] seconds to come to a complete stop when decelerating from [tex]\( 6 \, \text{m/s} \)[/tex] at a rate of [tex]\( 2 \, \text{m/s}^2 \)[/tex].
Hence, the time required for you to stop is [tex]\( 3 \)[/tex] seconds.
