Question

In the Daytona 500 auto race, a Ford Thunderbird and a Mercedes Benz are moving side by side down a straightaway at 67.5 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 67.5 m/s after a distance of 360 m. At this point how far has the Thunderbird fallen behind the Mercedes Benz, which has continued at a constant speed?

Answer 1

The Thunderbird slows down from 67.5 m/s to rest over a distance of 250 m

If v denotes the final velocity and u denotes the initial then,

where f is the de-acceleration and s is the stopping distance.

Putting the values,

Let the time required to stop is t1.

Then,

She stops at the pit for 5 s

The thunder bird then then accelerates from rest to a speed of 67.5 m/s over a distance of 360 m.

Let us calculate the acceleration for this movement.

Let it takes the car t3 to accelerate to this speed.

hence, total time de-accelerate over a distance of 250 m then to stop at the pit, and then moving 360 m is

The distance Benz had moved in this time interval is

Hence, the Thunderbird is behind the Benz by a distance of