Respuesta :
Answer:
1) 64.2 mi/h
2) 3.31 seconds
3) 47.5 m
4) 5.26 seconds
Explanation:
t = Time taken = 2.5 s
u = Initial velocity = 0 m/s
v = Final velocity = 21.7 m/s
s = Displacement
a = Acceleration
1) Top speed = 28.7 m/s
1 mile = 1609.344 m
[tex]1\ m=\frac{1}{1609.344}\ miles[/tex]
1 hour = 60×60 seconds
[tex]1\ s=\frac{1}{3600}\ hours[/tex]
[tex]28.7\ m/s=\frac{\frac{28.7}{1609.344}}{\frac{1}{3600}}=64.2\ mi/h[/tex]
Top speed of the cheetah is 64.2 mi/h
Equation of motion
[tex]v=u+at\\\Rightarrow a=\frac{v-u}{t}\\\Rightarrow t=\frac{21.7-0}{2.5}\\\Rightarrow a=8.68\ m/s^2[/tex]
Acceleration of the cheetah is 8.68 m/s²
2)
[tex]v=u+at\\\Rightarrow t=\frac{v-u}{a}\\\Rightarrow t=\frac{28.7-0}{8.68}\\\Rightarrow t=3.31\ s[/tex]
It takes a cheetah 3.31 seconds to reach its top speed.
3)
[tex]v^2-u^2=2as\\\Rightarrow s=\frac{v^2-u^2}{2a}\\\Rightarrow s=\frac{28.7^2-0^2}{2\times 8.68}\\\Rightarrow s=47.5\ m[/tex]
It travels 47.5 m in that time
4) When s = 120 m
[tex]s=ut+\frac{1}{2}at^2\\\Rightarrow 120=0\times t+\frac{1}{2}\times 8.68\times t^2\\\Rightarrow t=\sqrt{\frac{120\times 2}{8.68}}\\\Rightarrow t=5.26\ s[/tex]
The time it takes the cheetah to reach a rabbit is 120 m is 5.26 seconds
