To determine the cheetah's rate of acceleration, we can use the formula for acceleration:
[tex]\[ a = \frac{{v_f - v_i}}{t} \][/tex]
where:
- [tex]\( a \)[/tex] is the acceleration,
- [tex]\( v_f \)[/tex] is the final velocity,
- [tex]\( v_i \)[/tex] is the initial velocity,
- [tex]\( t \)[/tex] is the time taken.
Let's break down the problem step-by-step:
1. Identify the given values:
- Initial velocity ([tex]\( v_i \)[/tex]) = 0 m/s
- Final velocity ([tex]\( v_f \)[/tex]) = 25 m/s
- Time ([tex]\( t \)[/tex]) = 2.5 seconds
2. Substitute the given values into the formula:
[tex]\[ a = \frac{{25 \ \text{m/s} - 0 \ \text{m/s}}}{2.5 \ \text{s}} \][/tex]
3. Calculate the acceleration:
[tex]\[ a = \frac{25 \ \text{m/s}}{2.5 \ \text{s}} \][/tex]
[tex]\[ a = 10 \ \text{m/s}^2 \][/tex]
Thus, the cheetah's rate of acceleration is [tex]\( 10 \ \text{m/s}^2 \)[/tex].
Therefore, the correct answer is:
C. [tex]\( 10 \ \text{m/s}^2 \)[/tex]
