Question

A cheetah begins chasing after a gazelle. The cheetah starts from rest and quickly reaches its maximum speed of 27 m/s. If it took the cheetah 6 seconds to reach its maximum speed, how much ground did the cheetah cover?

Answer 1

The cheetah covered a distance of 81 meters.

Step-by-step explanation:

To calculate the ground covered by the cheetah, we need to find the distance it traveled while accelerating. We can use the equation for distance covered during uniform acceleration:

s = (vf2 - vi2) / (2a)

Where s is the distance, vf is the final velocity, vi is the initial velocity, and a is the acceleration.

In this case, the cheetah starts from rest, so the initial velocity is 0. The final velocity is 27 m/s, and the acceleration is the rate at which it reached that speed in 6 seconds. Plugging these values into the equation, we get:

s = (272 - 02) / (2 * (27/6))

Simplifying the equation:

s = (729 - 0) / (2 * 4.5)

s = 729 / 9

s = 81 meters