The problem below uses the same approximations you did in the lab and assumes that the lioness and the gazelle have constant accelerations until they reach their top speeds. Assume that both animals can maintain their respective top speeds for a long time.

The lioness is capable of accelerating for $5$ seconds and will continue to run at its top speed of $v^{\text{l}\text{i}\text{o}\text{n}}$ top $=10\mathrm{.}5\frac{m}{s}.$

The gazelle is capable of accelerating for $10$ seconds and will continue to run at its top speed of $v^{\text{g}\text{a}\text{z}\text{e}\text{l}\text{l}\text{e}}$ top $=16\frac{m}{s}.$

If the gazelle had a head start of $8$ m $,$ but no head start in time, calculate the time it'll take lioness, to catch the gazelle.

$5$

HINT$1$: You may find making the graphs of lioness' and gazelle's velocities vs$.$ time useful to think about this problem.

HINT$2$: Think about how the distance covered by each animal can be calculated using your velocity vs$.$ time graphs.