Question

In a 350-m race, runner A starts from rest and accelerates at 1.6 m/s^2 for the first 30 m and then runs at constant speed. Runner B starts from rest and accelerates at 2.0 m/s^2 for the first 30 m and then runs at constant speed. Runner A befins running as soon as the race begins but B first takes a nap to rest up. What is the longest nap that B can take and still not lose the race?

Answer 1

B can take 0.64 sec for the longest nap .

Step-by-step explanation:

Given that,

Total distance = 350 m

Acceleration of A = 1.6 m/s²

Distance = 30 m

Acceleration of B = 2.0 m/s²

We need to calculate the time for A

Using equation of motion

`s=ut+(1)/(2)at_(A)^2`

Put the value in the equation

`30=0+(1)/(2)*1.6* t_(A)^2`

`t_(A)=\sqrt{(30*2)/(1.6)}`

`t_(A)=6.12\ sec`

We need to calculate the time for B

Using equation of motion

`s=ut+(1)/(2)at_(B)^2`

Put the value in the equation

`30=0+(1)/(2)*2.0* t_(B)^2`

`t_(B)=\sqrt{(30*2)/(2.0)}`

`t_(B)=5.48\ sec`

We need to calculate the time for longest nap

Using formula for difference of time

`t'=t_(A)-t_(B)`

`t'=6.12-5.48`

`t'=0.64\ s`

Hence, B can take 0.64 sec for the longest nap .