Respuesta :
Answer:
Thunderbird is 995.157 meters behind the Mercedes
Explanation:
It is given that all the cars were moving at a speed of 71 m/s when the driver of Thunderbird decided to take a pit stop and slows down for 250 m. She spent 5 seconds in the pit stop.
Here final velocity [tex]v=0 \ m/s[/tex]
initial velocity [tex]u= 71 m/s[/tex] distance
Distance covered in the slowing down phase = [tex]250 m[/tex]
[tex]v^2-u^2=2as[/tex]
[tex]a= \frac {(v^2-u^2)}{2s}[/tex]
[tex]a = \frac {(0^2-71^2)}{(2 \times 250)}=-10.082 \ m/s^2[/tex]
[tex]v=u+at[/tex]
[tex]t= \frac {(v-u)}{a}[/tex]
[tex]= \frac {(0-71)}{(-10.082)}=7.042 s[/tex]
[tex]t_1=7.042 s[/tex]
The car is in the pit stop for 5s [tex]t_2=5 s[/tex]
After restart it accelerates for 350 m to reach the earlier velocity 71 m/s
[tex]a= \frac {(v^2-u^2)}{(2\times s)} = \frac{(71^2-0^2)}{(2 \times 370)} =6.81 \ m/s^2[/tex]
[tex]v=u+at[/tex]
[tex]t= \frac{(v-u)}{a}[/tex]
[tex]t= \frac{(71-0)}{6.81}= 10.425 s[/tex]
[tex]t_3=10.425 s[/tex]
total time= [tex]t_1 +t_2+t_3=7.042+5+10.425=22.467 s[/tex]
Distance covered by the Mercedes Benz during this time is given by [tex]s=vt=71 \times 22.467= 1595.157 m[/tex]
Distance covered by the Thunderbird during this time=[tex]250+350=600 m[/tex]
Difference between distance covered by the Mercedes and Thunderbird
= [tex]1595.157-600=995.157 m[/tex]
Thus the Mercedes is 995.157 m ahead of the Thunderbird.
