A cheetah can accelerate from rest to 24.1 m/s in 2.02 s.
a) Assuming the acceleration is constant over the time interval, what is the magnitude of
the acceleration of the cheetah?
b) What is the distance traveled by the cheetah in these 2.02 s?
c) A runner can accelerate from rest to 5.79 m/s in the same time, 2.02 s. What is the
magnitude of the acceleration of the runner?
d) By what factor is the cheetah's average acceleration magnitude greater than that of the
runner?
(a) 24.1m/s / 2.02s = 11.93 m/s^2
(b) s = 1/2 at^2
(c) 5.79/2.02 = 2.87 m/s^2
(d) 11.93/2.87 = ?
To calculate the answers to these questions, we need to use the kinematic equation:
v = u + at,
where:
- v is the final velocity (24.1 m/s for the cheetah),
- u is the initial velocity (0 m/s for both the cheetah and the runner),
- a is the acceleration,
- t is the time (2.02 s for both the cheetah and the runner).
a) To find the magnitude of acceleration for the cheetah, we rearrange the equation to solve for a:
a = (v - u) / t,
Substituting the given values:
a = (24.1 m/s - 0 m/s) / 2.02 s,
a = 11.94 m/s^2 (rounded to two decimal places).
Therefore, the magnitude of the cheetah's acceleration is 11.94 m/s^2.
b) To find the distance traveled by the cheetah, we can use the equation:
s = ut + 0.5at^2.
Since the cheetah starts from rest (u = 0), the equation simplifies to:
s = 0.5at^2.
Substituting the given values:
s = 0.5 * 11.94 m/s^2 * (2.02 s)^2,
s = 24.33 m (rounded to two decimal places).
Thus, the distance traveled by the cheetah is 24.33 meters.
c) To find the magnitude of acceleration for the runner, we can use the same formula as in part a:
a = (v - u) / t.
Substituting the given values for the runner:
a = (5.79 m/s - 0 m/s) / 2.02 s,
a = 2.87 m/s^2 (rounded to two decimal places).
So, the magnitude of the runner's acceleration is 2.87 m/s^2.
d) To determine how much greater the cheetah's acceleration is compared to the runner, we can calculate the acceleration ratio:
acceleration ratio = cheetah's acceleration / runner's acceleration,
acceleration ratio = 11.94 m/s^2 / 2.87 m/s^2,
acceleration ratio ≈ 4.16 (rounded to two decimal places).
Therefore, the cheetah's acceleration magnitude is approximately 4.16 times greater than that of the runner.