Question

In the Daytona 500 auto race, a Ford Thunderbird and a Mercedes Benz are moving side by side down a straightaway at 71.5 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 71.5 m/s after a distance of 350 m. At this point, how far has the Thunderbird fallen behind the Mercedes Benz, which has continued at a constant speed?

Answer 1

Answer:

957.4845 m

Explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

a = Acceleration

$v^2-u^2=2as\\\Rightarrow a=\frac{v^2-u^2}{2s}\\\Rightarrow a=\frac{0^2-71.5^2}{2\times 250}\\\Rightarrow a=-10.2245\ m/s^2$

$v=u+at\\\Rightarrow t=\frac{v-u}{a}\\\Rightarrow t=\frac{0-71.5}{-10.2245}\\\Rightarrow t=6.993\ s$

Time taken by the thunderbird to stop is 6.993 seconds

Time the thunderbird was at the pit is 5 seconds

$v^2-u^2=2as\\\Rightarrow a=\frac{v^2-u^2}{2s}\\\Rightarrow a=\frac{71.5^2-0^2}{2\times 350}\\\Rightarrow a=7.3\ m/s^2$

$v=u+at\\\Rightarrow t=\frac{v-u}{a}\\\Rightarrow t=\frac{71.5-0}{7.3}\\\Rightarrow t=9.79\ s$

Time taken to accelerate back to 71.5 m/s is 9.79 seconds

Total time to this point is 6.993+5+9.79 = 21.783 seconds

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

Distance = Speed × Time

⇒Distance = 71.5 × 21.783 = 1557.4845 m

The thunderbird has covered 250+350 = 600 m

So, the distance between them is 1557.4845-600 = 957.4845 m