Question

A cheetah can accelerate at 3 m/s for 10 seconds, then run for another 10 seconds at a constant speed. A gazelle is 10 meters from the cheetah traveling at a constant speed of 20 m/s. Will the cheetah catch the gazelle? If so, how far has the cheetah run? If not, what is the closest the cheetah will get to the gazelle?

Answer 1

The cheetah will catch the gazelle. The cheetah will run a total distance of 180 meters.

Step-by-step explanation:

The cheetah will catch the gazelle. To determine how far the cheetah has run, we need to calculate the distance covered in each phase of its motion.

During the acceleration phase, the cheetah accelerates at 3 m/s² for 10 seconds, so the distance covered is given by the equation d = 0.5 * a * t² where d is the distance, a is the acceleration, and t is the time. Plugging in the values, we get d = 0.5 * 3 * 10² = 150 meters.

During the constant speed phase, the cheetah travels for another 10 seconds at a constant speed of 3 m/s. Therefore, the distance covered is d = v * t = 3 * 10 = 30 meters.

In total, the cheetah has run 150 + 30 = 180 meters.