To solve this problem, we need to find the time it takes for car A to surpass car B and then calculate the distance traveled by both cars at that time.
Let's denote the time at which car A surpasses car B as t (in seconds). At this time, both cars will have traveled the same distance.
For car B: Distance traveled by car B = Velocity × Time Distance_B = 20 m/s × t
For car A: Distance traveled by car A = Initial Velocity × Time + (1/2) × Acceleration × Time^2 Distance_A = 0 + (1/2) × 2 m/s^2 × t^2 Distance_A = t^2 m
Since the distances traveled by both cars are equal at time t, we can set up an equation:
Distance_A = Distance_B t^2 = 20t
Simplifying the equation: t^2 - 20t = 0 t(t - 20) = 0
So, either t = 0 (which is the initial condition) or t - 20 = 0.
If we take t = 0, it corresponds to the initial condition where car A is at rest and car B is 50 meters away. Therefore, we discard t = 0 as a valid solution.
If we take t - 20 = 0, we get t = 20 seconds.
Now, let's calculate the distance traveled by both cars when t = 20 seconds:
Distance_A = t^2 = (20)^2 = 400 meters Distance_B = 20 m/s × t = 20 m/s × 20 s = 400 meters
Therefore, when car A surpasses car B, they will both have traveled a distance of 400 meters.