Question

A tiger running $100m$ race, accelerates for one third time of the total time and then moves with uniform speed. Then find the total time taken by the tiger to run $100m$ if the acceleration of the tiger is $8m/s^2$:

Answer 1

$\frac{3v_0}{T}=8$

$\frac{v_0}{T}=\frac{8}{3}$

$\frac{1}{2}\times v_0\times \frac{T}{3}+v_0\frac{2T}{3}=100$

$\frac{v_{0}T}{6}+\frac{2v_{0}T}{3}=100$

$\frac{v_{0}T+4v_{0}T}{6}=100$

$\frac{5v_{0}T}{6}=100$

$v_{0}T=\frac{100}{8}\times 6$

$v_{0}T=120$

$\frac{v_0}{T}=\frac{8}{3}$

$\frac{v_{0}T}{\frac{v_0}{T}}=\frac{120\times 3}{8}$

$T^2=45$

$T=\sqrt{45}$

$T=6.708s$