Motion in one dimension of a swimmer

[Alice-Shallom]

Hi, i need help with the following:

One swimmer in a relay race has a 0.50-s lead and is swimming at a constant speed of 4.0 m/s. He has 50 m to swim before reaching the end of the pool. A second swimmer moves in the same direction as the leader. What constant speed must the second swimmer have in order to catch up to the leader at the end of the pool?

I understand that since the 1st swimmer swims at constant speed, he has zero accelaration.

Is it useful to use this formula? Speed = Distance / Time
If not, which formula can i use?

Thanks.

 

[Doc Al]

Both swimmers swim at constant speeds. And, yes, V = D/T will be very useful.

Ask yourself: How much of a lead (in distance) does the first swimmer have? How long is the pool? How long will it take the first swimmer to reach the end?

Then ask: How fast must the second swimmer swim if he is to get all the way across the pool in the same time that the first swimmer takes to swim 50 m?

 

[M98Ranger]

To find the constant speed that the second swimmer must have in order to catch up to the leader, we can use the formula for distance: d = rt, where d is the distance, r is the rate (or speed), and t is the time. In this case, we know that the distance is 50 m and the time is 0.50 s for the first swimmer. Plugging these values into the formula, we get:

50 m = (4.0 m/s)t

Solving for t, we get t = 12.5 s.

Since the second swimmer needs to catch up to the leader at the end of the pool, their distance and time will be the same. We can set up a similar equation for the second swimmer:

50 m = (rs)t

Where r is the unknown speed of the second swimmer and s is the same time of 12.5 s. Solving for r, we get:

r = 4.0 m/s

Therefore, the second swimmer must also swim at a constant speed of 4.0 m/s in order to catch up to the leader at the end of the pool. This makes sense since both swimmers are covering the same distance in the same amount of time, they must have the same speed in order to reach the end at the same time.

In summary, we can use the formula d = rt to solve for the speed of the second swimmer, since they are both covering the same distance in the same amount of time. I hope this helps!