To determine the minimum time that car B should be at rest so that car A finishes first, we need to compare the time it takes for each car to cover the given distance of 1000m.
Let's calculate the time it takes for car A and car B to cover the distance:
For car A: Distance (s) = 1000m Velocity (v) = 50m/s
Time (t_A) taken by car A to cover the distance is given by the equation:
t_A = s / v t_A = 1000m / 50m/s t_A = 20 seconds
So, car A takes 20 seconds to cover the distance.
Now, let's consider the scenario where car B is at rest for a certain amount of time (t_rest). In this case, car B will start moving only after the time t_rest has passed.
For car B: Distance (s) = 1000m Velocity (v) = 80m/s
Time (t_B) taken by car B to cover the distance is given by:
t_B = s / v t_B = 1000m / 80m/s t_B = 12.5 seconds
Now, to ensure car A finishes first, the condition is t_A < t_B. We need to find the minimum time that car B should be at rest, which means t_B should be greater than t_A. Therefore:
t_B > t_A 12.5 seconds > 20 seconds
As 12.5 seconds is already smaller than 20 seconds, it is not possible for car B to be at rest and still finish after car A. Car B's initial velocity of 80m/s is already greater than car A's velocity of 50m/s, so car B will finish covering the distance before car A regardless of any rest time.