Question

A tiger running 100 m race, accelerates for one third time of the total tim
slerates for one third time of the total time and then moves with uniform
tal time taken by the tiger to run 100 m if the acceleration of the tiger is 8m/s?

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Answer 1

Given that,

Acceleration = 8 m/s²

Distance = 100 m

Time = one third time of the total time

We need to calculate the half distance

Using equation of motion

$s_{1}=ut+\dfrac{1}{2}at^2$

Put the value into the formula

$s_{1}=0+\dfrac{1}{2}\times8\times(\dfrac{t}{3})^2$

$s_{1}=\dfrac{4t^2}{9}$....(I)

When tiger moves with uniform,

We need to calculate the velocity

Using equation of motion

$v=u+at_{1}$

$v=0+8\dfrac{t}{3}$

We need to calculate the distance

Using equation of motion

$s_{2}=v\times 2t$

Put the value into the formula

$s_{2}=8\dfrac{t}{3}\times2\times\dfrac{t}{3}$

$s_{2}=\dfrac{16t^2}{9}$....(II)

We need to calculate the total time

Using formula of total distance

$s=s_{1}+s_{2}$

Put the value in to the formula

$100=\dfrac{4t^2}{9}+\dfrac{16t^2}{9}$

$100=\dfrac{20t^2}{9}$

$t=\dfrac{100\times9}{20}$

$t=\sqrt{45}$

$t=6.7 sec$

Hence, The total time will be 6.7 sec.