Question

A cheetah waits in hiding behind a bush. The cheetah spots a gazelle running past at 10 m/s. At the instant the gazelle passes the cheetah, the cheetah accelerates from rest at 4 m/s2 to catch the gazelle. (i) How long does it take the cheetah to catch the gazelle? (ii) What is the displacement of the gazelle and cheetah?

Answer 1

The time for both is equal. The distance for both is equal. So, for the cheetah and gazelle correspondingly, we have

$$d=\frac{at^2}{2},\\\space\\ d=vt.\\\space\\ vt=\frac{at^2}{2},\\\space\\ t=\frac{2v}{a}=5\text{ s}.\\ d=vt=10·5=50\text{ m}.$$