The cheetah can reach a top speed of 114 km/h (71 mi/h). While chasing its prey in a short sprint, a cheetah starts from rest and runs 46 m in a straight line, reaching a final speed of 73 km/h.
To find out the acceleration of the cheetah, we can use the equation:
(v^2 - u^2) = 2as
Where:
v = final velocity
u = initial velocity
a = acceleration
s = displacement
We are given:
v = 73 km/h
u = 0 km/h (since it starts from rest)
s = 46 m
First, we need to convert the velocities to m/s since the displacement is given in meters:
v = 73 km/h * (1000 m/1 km) * (1 h/3600 s) = 20.28 m/s
u = 0 km/h * (1000 m/1 km) * (1 h/3600 s) = 0 m/s
Now we can plug these values into the equation:
(20.28^2 - 0^2) = 2a * 46
414.79 = 92a
Dividing both sides by 92:
a = 414.79/92 = 4.51 m/s^2
Therefore, the acceleration of the cheetah as it chases its prey is approximately 4.51 m/s^2.