To find the acceleration of the plane, we use the formula for acceleration:
[tex]\[ a = \frac{\Delta v}{\Delta t} \][/tex]
where:
- [tex]\( a \)[/tex] is the acceleration,
- [tex]\(\Delta v\)[/tex] is the change in velocity,
- [tex]\(\Delta t\)[/tex] is the change in time.
Given:
- The initial speed ([tex]\( v_i \)[/tex]) of the plane is [tex]\( 245 \, \text{m/s} \)[/tex].
- The final speed ([tex]\( v_f \)[/tex]) of the plane is [tex]\( 230 \, \text{m/s} \)[/tex].
- The time ([tex]\( \Delta t \)[/tex]) it takes to slow down is [tex]\( 7 \, \text{s} \)[/tex].
First, calculate the change in velocity ([tex]\(\Delta v\)[/tex]):
[tex]\[ \Delta v = v_f - v_i = 230 \, \text{m/s} - 245 \, \text{m/s} = -15 \, \text{m/s} \][/tex]
Next, use the acceleration formula:
[tex]\[ a = \frac{\Delta v}{\Delta t} = \frac{-15 \, \text{m/s}}{7 \, \text{s}} \approx -2.142857142857143 \, \text{m/s}^2 \][/tex]
Finally, round the acceleration to the nearest hundredth:
[tex]\[ a \approx -2.14 \, \text{m/s}^2 \][/tex]
Therefore, the correct answer is:
[tex]\[ -2.14 \, \text{m/s}^2 \][/tex]
Hence, the acceleration of the plane is [tex]\( -2.14 \, \text{m/s}^2 \)[/tex].
