One swimmer in a relay race has a 0.50 s lead and is...

One swimmer in a relay race has a 0.50 s lead and is swimming at a constant speed of $4.00 \mathrm{m} / \mathrm{s}$. The swimmer has $50.0 \mathrm{m}$ 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?

Key Concepts

Uniform Motion

Uniform motion refers to movement at a constant speed in a straight line, meaning there is no acceleration or deceleration. In problems that involve uniform motion, the relationship between distance, speed, and time is linear, which allows the use of the formula distance = speed × time without the need to account for changing speeds.

Relative Motion

Relative motion involves analyzing the movement of one object with respect to another. In scenarios where two objects start at different times or positions, comparing their distances traveled over the same time period helps determine conditions for one object to overtake or catch up to the other.

Time, Speed, and Distance Relationship

The fundamental relationship between time, speed, and distance is central to solving kinematics problems. This relationship, expressed as distance = speed × time, allows one to set up equations for each moving object. By equating the time and distance for two objects, one can determine unknown variables such as the required speed needed for one object to catch up with another.

Time Lag

Time lag refers to the delay between the start times of two events or moving objects. In many motion problems, one object may start its motion later than another. This difference in starting times must be taken into account when setting up the problem, as it affects how long each object has to travel a certain distance and consequently influences the calculation for when or where they might meet.

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