ANSWER:
1.3 times faster
STEP-BY-STEP EXPLANATION:
Given:
Distance ostrich = 56 m
Time ostrich = 14.5 s
Initial velocity = 0 m/s
To calculate the final velocity of the ostrich we use the following formula:
[tex]\begin{gathered} d=0.5(v_f+v_i)\Delta t \\ \\ \text{ we solve for }v_f \\ \\ 56=0.5(0+v_f)14.5 \\ \\ 56=7.25v_f \\ \\ v_f=\frac{56}{7.25}=7.7\text{ m/s} \end{gathered}[/tex]Now, we calculate the average velocity of the ostrich, like this:
[tex]\begin{gathered} v_o=\frac{v_i+v_f}{2}=\frac{0+7.7}{2} \\ \\ v_o=3.9\text{ m/s} \end{gathered}[/tex]We calculate the time it would take the ostrich to travel 100 meters with the following formula:
[tex]\begin{gathered} d=0.5(v_{f}+v_{i})\Delta t \\ \\ \text{ we replacing} \\ \\ 100=0.5\left(0+7.7\right)\Delta t \\ \\ \Delta t=25.9\text{ sec} \end{gathered}[/tex]now we calculate the time of the cheetah knowing that it takes 5.7 seconds less:
[tex]\begin{gathered} t_c=t_o-5.7 \\ \\ t_c=25.9-5.7=20.2\text{ sec} \end{gathered}[/tex]Now, we can calculate the final velocty of the cheetah using the following formula:
[tex]\begin{gathered} d=0.5(v_{f}+v_{i})\Delta t \\ \\ \text{ we replacing} \\ \\ 100=0.5\left(v_f+0\right)20.2 \\ \\ v_f=\frac{100}{10.1} \\ \\ v_f=9.9\text{ m/s} \end{gathered}[/tex]Now we calculate the average velocity, like this:
[tex]\begin{gathered} v_c=\frac{v_i+v_f}{2}=\frac{0+9.9}{2} \\ \\ v_c=4.95\text{ m/s} \end{gathered}[/tex]we calculate the ratio between the two to know how many times the cheetah is faster:
[tex]r=\frac{4.95}{3.9}=1.3[/tex]Therefore, the cheetah is 1.3 times faster than the ostrich.