Question

In the Daytona 500 auto race, a Ford Thunderbird and a Mercedes Benz are moving side by side down a straightaway at 68.0 m/s. The driver of the Thunderbird realizes that she must make a pit stop, and she smoothly slows to a stop over a distance of 250 m. She spends 5.00 s in the pit and then accelerates out, reaching her previous speed of 68.0 m/s after a distance of 420 m. At this point how far has the Thunderbird fallen behind the Mercedes Benz, which has continued at a constant speed?

Answer 1

1010 m

Step-by-step explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

a = Acceleration

`v^2-u^2=2as\\\Rightarrow a=(v^2-u^2)/(2s)\\\Rightarrow a=(0^2-68^2)/(2* 250)\\\Rightarrow a=-9.248\ m/s^2`

`v=u+at\\\Rightarrow t=(v-u)/(a)\\\Rightarrow t=(0-68)/(-9.248)\\\Rightarrow t=7.35\ s`

Time taken by the thunderbird to stop is 7.35 seconds

Time the thunderbird was at the pit is 5 seconds

`v^2-u^2=2as\\\Rightarrow a=(v^2-u^2)/(2s)\\\Rightarrow a=(68^2-0^2)/(2* 420)\\\Rightarrow a=5.5\ m/s^2`

`v=u+at\\\Rightarrow t=(v-u)/(a)\\\Rightarrow t=(68-0)/(5.5)\\\Rightarrow t=12.36\ s`

Time taken to accelerate back to 68 m/s is 12.36 seconds

Total time to this point is 7.35+5+12.36 = 24.71 seconds

The Mercedes Benz is moving at a constant velocity hence it has no acceleration and we use the formula

Distance = Speed × Time

⇒Distance = 68 × 24.71 = 1680 m

The thunderbird has covered 250+420 = 670 m

So, the distance between them is 1680-670 = 1010 m