Calculating the Average Acceleration of a Cheetah

Calculating Average Acceleration

The average acceleration of a cheetah during a sprint where it achieves 97 km/h over 48 meters is calculated using kinematic equations to be 7.54 m/s².

Explanation

The question asks us to determine the average acceleration of a cheetah during a short sprint where it starts from rest and reaches a final speed of 97 km/h (which equals 26.94 m/s) over a distance of 48 meters. To find the acceleration, we can use the kinematic equation:

v² = u² + 2as

Where:
v is the final velocity,
u is the initial velocity,
a is the acceleration, and
s is the displacement.

The cheetah starts from rest, so u = 0. Rearranging the equation for acceleration, we get:

a = (v² - u²)/(2s)

Substituting the values:
a = (26.942 - 0²)/(2 × 48)
a = 723.6836/96
a = 7.54 m/s²

Thus, the cheetah's average acceleration during the sprint is 7.54 m/s².