   Chapter 2, Problem 41P

Chapter
Section
Textbook Problem

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 in. 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?

To determine
The distance the thunderbird fallen behind.

Explanation

Given Info: The initial speed of Ford Thunderbird and Mercedes Benz is 71.5m/s , the distance covered by the Thunderbird after a pit stop is 250m , duration of Thunderbird in the pit is 5.00s , and the distance covered by Thunderbird when she reaching her previous speed is 350m .

Explanation:

The formula used to calculate the time taken by the thunderbird to slow down is,

Δt1=Δx1((v0+v)2)

Here,

Δx1 is the displacement

v0 is the initial velocity

v is the final velocity

Δt1 is the time taken to slow down

Substitute 250m for Δx1 , 0 for v0 , and 71.5m/s for v to find Δt1 .

Δt1=250m((0+(71.5m/s))2)=6.99s

Thus, the time taken by the thunderbird to slow down is 6.99s .

The formula used to calculate the time taken by the thunderbird to slow down is,

Δt2=Δx2((v0+v)2)

Here,

Δx2 is the displacement

v0 is the initial velocity

v is the final velocity

Δt2 is the time taken to slow down

Substitute 6.99s for Δt1 , 9.79s for Δt2 , and 5.00s for Δt3 to find Δt .

Δt=6.99s+9.79s+5.00s=21.8s

Thus, the total time is 21.8s .

The formula used to calculate the total distance travelled by the Mercedes is,

ΔxM=vΔt

Here,

ΔxM is the distance travelled by the Mercedes

Substitute 71

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