Practice Problems Sol4

Problem 4 Solution: Two cars are moving at constant velocity to the right. At time = 0, car A is 25 m ahead of car B. Car A has a velocity of 20 m/s and car B has a velocity of 25 m/s. Draw a motion map for the two cars up to time = 10 sec. Explain how you can determine when car B catches up to car A.

With a motion map drawn carefully to scale like the one above, you can see that the fifth pair of dots line up, indicating that B catches up to A at t = 5 sec. You can also solve the problem by recognizing that B is traveling with a velocity 5 m/s greater than the velocity of A. Thus, in each second, B will gain 5 meters on A. In five seconds B will have gained 25 meters and will have caught up to A. A third way of answering the problem is algebraically: Goal: You want to find the time corresponding to when B's displacement equals A's displacement plus 25 m. As an equation: displacement of B = displacement of A + 25 m We can use the constant velocity mathematical relationship to find each displacement: displacement of B = (velocity of B) x time displacement of A = (velocity of A) x time Substituting: (velocity of B) x time = (velocity of A) x time + 25 m Solving for time: time = (25 m) / ( velocity of B - velocity of A) = (25 m) / (5 m/s) = 5 s