A tiger running $100 m$ 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 $100 m$ if the acceleration of the tiger is $8 m / s^{2}$ :

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Solution

$\frac{3 v_{0}}{T} = 8$
$\frac{v_{0}}{T} = \frac{8}{3}$
$\frac{1}{2} \times v_{0} \times \frac{T}{3} + v_{0} \frac{2 T}{3} = 100$
$\frac{v_{0} T}{6} + \frac{2 v_{0} T}{3} = 100$
$\frac{v_{0} T + 4 v_{0} T}{6} = 100$
$\frac{5 v_{0} T}{6} = 100$
$v_{0} T = \frac{100}{8} \times 6$
$v_{0} T = 120$
$\frac{v_{0}}{T} = \frac{8}{3}$
$\frac{v_{0} T}{\frac{v_{0}}{T}} = \frac{120 \times 3}{8}$
$T^{2} = 45$
$T = \sqrt{45}$
$T = 6.708 s$

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A tiger running 100 m 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 100 m if the acceleration of the tiger is 8m/s2:

3v0T=8v0T=8312×v0×T3+v02T3=100v0T6+2v0T3=100v0T+4v0T6=1005v0T6=100v0T=1008×6v0T=120v0T=83v0Tv0T=120×38T2=45T=√45T=6.708s

A tiger running $100 m$ 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 $100 m$ if the acceleration of the tiger is $8 m / s^{2}$ :