contestada

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?

Respuesta :

Answer:

B can take 0.64 sec for the longest nap .

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

[tex]s=ut+\dfrac{1}{2}at_{A}^2[/tex]

Put the value in the equation

[tex]30=0+\dfrac{1}{2}\times1.6\times t_{A}^2[/tex]

[tex]t_{A}=\sqrt{\dfrac{30\times2}{1.6}}[/tex]

[tex]t_{A}=6.12\ sec[/tex]

We need to calculate the time for B

Using equation of motion

[tex]s=ut+\dfrac{1}{2}at_{B}^2[/tex]

Put the value in the equation

[tex]30=0+\dfrac{1}{2}\times2.0\times t_{B}^2[/tex]

[tex]t_{B}=\sqrt{\dfrac{30\times2}{2.0}}[/tex]

[tex]t_{B}=5.48\ sec[/tex]

We need to calculate the time for longest nap

Using formula for difference of time

[tex]t'=t_{A}-t_{B}[/tex]

[tex]t'=6.12-5.48[/tex]

[tex]t'=0.64\ s[/tex]

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

Otras preguntas