Mathematics: two drivers, alison and kevin, are participating in a drag race. beginning from a standing start, they each proceed with a constant acceleration. alison covers the last 1/4 of the distance in 3 seconds, whereas kevin overs the last 1/3 of the distance in 4 seconds. who wins and by how much time?

-1 trustStep-by-step explanation:...

two drivers, alison and kevin, are participating

Alexmills6093

15.01.2022

Alison wins against Kevin by 0.93 s

Step-by-step explanation:

Alison covers the last 1/4 of the distance in 3 seconds, at a constant acceleration a_a , we have the following equation of motion

s/4 = a_at_a^2/2

where s (m) is the total distance, ta = 3 s is the time

s = 4a_a3^2/2 = 18a_a

a_a = s/18

Similarly, Kevin overs the last 1/3 of the distance in 4 seconds, at a constant acceleration a_k , we have the following equation of motion:

s/3 = a_kt_k^2/2

tk = 4 s is the time

s = 3a_k4^2/2 = 24a_k

a_k = s/24

Since a_a = s/18 we can conclude that a_a a_k , so Alison would win.

The time it takes for Alison to cover the entire track

s = a_aT_a^2/2

T_a^2 = 2s/a_a = 2s/(s/18) = 36

$T_a = \sqrt{36} = 6 s$

The time it takes for Kevin to cover the entire track

s = a_kT_k^2/2

T_k^2 = 2s/a_k = 2s/(s/24) = 48

$T_a = \sqrt{48} = 6.93 s$

So Alison wins against Kevin by 6.93 - 6 = 0.93 s

0,0(0 оценок)