To solve for the acceleration of Desmond's car, we use the formula for acceleration:
[tex]\[ a = \frac{\Delta v}{t} \][/tex]
where:
- [tex]\( a \)[/tex] is the acceleration,
- [tex]\( \Delta v \)[/tex] is the change in velocity,
- [tex]\( t \)[/tex] is the time over which the change occurs.
In this problem, we are given the following values:
- Initial velocity ([tex]\( v_i \)[/tex]) is [tex]\( 20 \)[/tex] meters/second.
- Final velocity ([tex]\( v_f \)[/tex]) is [tex]\( 10 \)[/tex] meters/second.
- Time ([tex]\( t \)[/tex]) is [tex]\( 5 \)[/tex] seconds.
First, we need to find the change in velocity ([tex]\( \Delta v \)[/tex]):
[tex]\[ \Delta v = v_f - v_i \][/tex]
Substituting the given values:
[tex]\[ \Delta v = 10 \, \text{meters/second} - 20 \, \text{meters/second} \][/tex]
[tex]\[ \Delta v = -10 \, \text{meters/second} \][/tex]
Next, we substitute [tex]\(\Delta v\)[/tex] and [tex]\( t \)[/tex] into the acceleration formula:
[tex]\[ a = \frac{\Delta v}{t} \][/tex]
[tex]\[ a = \frac{-10 \, \text{meters/second}}{5 \, \text{seconds}} \][/tex]
[tex]\[ a = -2 \, \text{meters/second}^2 \][/tex]
Therefore, the acceleration of the car is [tex]\( -2 \, \text{meters/second}^2 \)[/tex]. This negative sign indicates that the car is decelerating.
The correct answer is:
C. [tex]\( -2 \, \text{meters/second}^2 \)[/tex]
