Final answer:
Physics principles are applied to determine when two runners have the same velocity. Specifically, the problem involves relative velocity, and additional context is necessary for the exact timing. If runners begin at the same location and point in time, the faster runner will eventually match the velocity of the slower runner if no initial separation distance exists.
Step-by-step explanation:
The question of when runners have the same velocity pertains to the concept of relative velocity in Physics. To find the instance when runners have the same velocity, the problem can be set up using the principle that the relative velocity between the two runners is the difference in their individual velocitiesAccording to the information given, runner A has a velocity of 3.50 m/s and runner B has a velocity of 4.20 m/s. To find out how long after the race began do the runners have the same velocity, one would typically calculate the time it takes for runner B to close the gap between them, which would happen when their relative velocities result in runner B catching up to A. However, we cannot provide a precise answer without additional context, such as a specific time or distance over which we should calculate these velocitiesThat said, if we consider a hypothetical scenario where runners start together and maintain a constant velocity throughout the race, runner B would catch up to runner A when the time multiplied by the relative velocity (which is 0.70 m/s, the difference between 4.20 m/s and 3.50 m/s) equals the initial separation distance.
This assumes the separation is the only factor and that the runners start at the same point.To find the time at which the runners have the same velocity, we need to calculate their positions at different times and determine when their positions are equal.Let's assume that runner A starts at time t0 and runner B starts at time t = 2.5 s. Both runners reach a distance of 64 m from the starting point at time t = 25 s. If their speeds remain constant, we can use the equation d = v * t, where d is the distance, v is the velocity, and t is the time.Using this equation, we can calculate the positions of the runners at different times. Runner A's position at time t = 45 s is given by dA = vA * (t - t0) = vA * (45 - t0). Runner B's position at time t = 45 s is given by dB = vB * (t - 2.5) = vB * (45 - 2.5).To find the time at which the runners have the same velocity, we set dA equal to dB and solve for t: vA * (45 - t0) = vB * (45 - 2.5).Solving this equation will give us the time at which the runners have the same velocity.