Let's solve the problem step-by-step to find the cyclist's acceleration.
1. Understand the given values:
- Initial velocity ([tex]\( u \)[/tex]): [tex]\( 8 \, \text{m/s} \)[/tex]
- Final velocity ([tex]\( v \)[/tex]): [tex]\( 3 \, \text{m/s} \)[/tex]
- Time ([tex]\( t \)[/tex]): [tex]\( 1 \, \text{minute} \)[/tex]
2. Convert time to seconds:
Since time is given in minutes, we need to convert it to seconds.
[tex]\[
1 \, \text{minute} = 60 \, \text{seconds}
\][/tex]
So, [tex]\( t = 60 \, \text{seconds} \)[/tex].
3. Use the formula for acceleration ([tex]\( a \)[/tex]):
The formula to calculate acceleration is:
[tex]\[
a = \frac{v - u}{t}
\][/tex]
where:
- [tex]\( v \)[/tex] is the final velocity.
- [tex]\( u \)[/tex] is the initial velocity.
- [tex]\( t \)[/tex] is the time taken.
4. Substitute the given values into the formula:
[tex]\[
a = \frac{3 \, \text{m/s} - 8 \, \text{m/s}}{60 \, \text{seconds}}
\][/tex]
5. Calculate the acceleration:
[tex]\[
a = \frac{-5 \, \text{m/s}}{60 \, \text{seconds}}
= -0.08333333333333333 \, \text{m/s}^2
\][/tex]
So, the cyclist's acceleration is [tex]\(-0.08333333333333333 \, \text{m/s}^2\)[/tex].
Among the given options, the closest match to [tex]\(-0.08333333333333333 \, \text{m/s}^2\)[/tex] is:
[tex]\[ -0.08 \, \text{m/s}^2 \][/tex]
Therefore, the correct answer is:
[tex]\[ -0.08 \, \text{m/s}^2 \][/tex]
